“By hanging a halt in this critical funding over states like a sword of Damocles, defendants impose immense harm on states,” they argued in one of the suits, “forcing them to choose between readiness for disasters and emergencies, on the one hand, and their judgment about how best to investigate and prosecute crimes, on the other.”

Rob Bonta, the attorney general of California, who is spearheading the litigation, added in a statement that President Trump was treating vital funding as a “bargaining chip.”

The White House announced two executive orders last month threatening to cut off funding to so-called sanctuary jurisdictions if they didn’t fully cooperate with immigration authorities.

Asked about the lawsuits, Kush Desai, a White House spokesman, said: “Americans would all be better off if these Democrat attorneys general focused on prosecuting criminals and working with the Trump administration to address the toll of gangster illegal aliens on their communities instead of playing political games.”

The states’ attorneys general filed both lawsuits — one naming the Federal Emergency Management Agency and the Department of Homeland Security and the other the Transportation Department — in Federal District Court in Rhode Island.

California, Illinois, New Jersey and Rhode Island are leading both lawsuits. Maryland is also listed as a lead state in the transportation lawsuit.

Joining them on both suits are Colorado, Connecticut, Delaware, Hawaii, Maine, Massachusetts, Michigan, Minnesota, Nevada, New Mexico, New York, Oregon, Vermont, Washington and Wisconsin. All of the states have Democratic attorneys general and governors, except for Nevada and Vermont, which have Republican governors.

A similar lawsuit was filed a few weeks ago by a coalition of 19 states over the administration’s threat to withhold federal funding from states and school districts that have certain diversity programs in their public schools.

State attorneys general have also sued over tariffs, and mass firings at agencies such as the Education and Health and Human Services Departments.

Judge Dugan, who has been temporarily removed from the bench by the Wisconsin Supreme Court while the case against her advances, has indicated through a lawyer that she intends to fight the charges. She is expected to appear in court on Thursday.

“Judge Hannah C. Dugan has committed herself to the rule of law and the principles of due process for her entire career as a lawyer and a judge,” her lawyers said in a statement shortly after she was arrested. They added on Tuesday that “Judge Dugan asserts her innocence and looks forward to being vindicated in court.”

The indictment was announced during a short hearing on Tuesday evening at the federal courthouse in downtown Milwaukee. After 20 members of a grand jury entered a wood-paneled courtroom and took their seats, a judge examined paperwork and indicated that Judge Dugan, along with other defendants in unrelated cases, had been indicted.

Judge Dugan’s transformation from a little-known local jurist to a face of the national immigration debate began on April 18 with a pretrial hearing in a domestic abuse case against Eduardo Flores-Ruiz, a Mexican immigrant.

Several federal officials from different agencies had gathered in the hallway outside Judge Dugan’s courtroom and had planned to arrest Mr. Flores-Ruiz, who they said was in the country illegally, after his court appearance. The federal agents had told courthouse security officers and the judge’s courtroom deputy about their plans, according to an F.B.I. charging document.

When Judge Dugan became aware of the federal agents, the charging document said, she became “visibly upset and had a confrontational, angry demeanor.” According to the criminal complaint, the judge confronted the agents and told them to talk to the chief judge of the courthouse. She then returned to her courtroom and, according to the charging document, directed Mr. Flores-Ruiz through a different exit than the public door that led to the hallway where agents were waiting.

“Despite having been advised of the administrative warrant for the arrest of Flores-Ruiz, Judge Dugan then escorted Flores-Ruiz and his counsel out of the courtroom through the ‘jury door,’ which leads to a nonpublic area of the courthouse,” according to the complaint, which was written by an F.B.I. agent.

Mr. Flores-Ruiz made it outside the courthouse, the charging document said, where a Drug Enforcement Administration agent spotted him. Agents approached him on the street outside the courthouse. “A foot chase ensued,” the complaint said. “The agents pursued Flores-Ruiz for the entire length of the courthouse” before catching and arresting him, the complaint said. Federal agents said Mr. Flores-Ruiz was removed from the United States in 2013 and that there was no record of him seeking or receiving permission to return.

Judge Dugan was arrested and charged with obstructing a proceeding of a federal agency, and concealing an individual to prevent his discovery and arrest.

The arrest of the judge marked an escalation of the Trump administration’s warnings that local officials must not impede federal efforts to deport millions of undocumented immigrants. Attorney General Pam Bondi and other administration officials have defended the case against Judge Dugan.

“It doesn’t matter what line of work you are in, if you break the law, we will follow the facts and we will prosecute you,” Ms. Bondi said in a video.

Elected Democrats in Wisconsin and beyond have criticized the case against the judge and accused prosecutors of politicizing the situation. And earlier this month, more than 150 former state and federal judges signed a letter to Ms. Bondi calling the arrest of Judge Dugan an attempt to intimidate the judiciary.

“This cynical effort undermines the rule of law,” that letter said, “and destroys the trust the American people have in the nation’s judges to administer justice in the courtrooms and in the halls of justice across the land.”

Julie Bosman contributed reporting.

The indictment charged a father and son — Pedro Inzunza Noriega, 62, and Pedro Inzunza Coronel, 33 — with violating terrorism statutes while running a drug business that reached from Mexico to Guatemala, Panama and Costa Rica. The two men were leaders of the Beltrán-Leyva faction of the cartel, prosecutors said, and were named in the indictment with five of their subordinates, who were not accused of terrorism offenses.

The nine-page charging document did not include any details about how the men had engaged in the alleged narco-terrorism. It remains to be seen whether the case against them will reveal any evidence supporting the terrorism charges that go beyond the administration’s decision to identify the Sinaloa cartel as a terrorist organization.

Trump administration officials have also designated other criminal mafias as terrorist groups, including Mexican drug gangs like the Jalisco New Generation Cartel and more traditional street gangs like Tren de Aragua, which is based in Venezuela, and the Salvadoran group known as MS-13.

Over the past several years, prosecutors claim, Mr. Inzunza Noriega and his son trafficked tens of thousands of kilograms of fentanyl into the United States. In December, they said, Mexican law enforcement officials raided multiple locations in Sinaloa that were controlled and managed by the men, discovering nearly 20 million doses of the drug in what was described as a record seizure.

At the time, President Claudia Sheinbaum of Mexico said the operations were part of a long investigation and had resulted in “the largest mass seizure of fentanyl pills ever made.” She added that the operation had seized more than a ton of fentanyl pills worth nearly $400 million.

U.S. law enforcement officials have generally supported the idea of designating drug cartels as terrorist organizations — if only because it gives prosecutors the ability to charge cartel defendants under powerful federal statutes that often carry stiff penalties.

But prosecutors have not yet had to defend such charges in court and may face pushback not only from defense lawyers, but also from judges overseeing such cases.

Prosecutors have traditionally relied on drug conspiracy charges to go after cartel operatives.

Last week, for example, Ovidio Guzmán López, one of four sons of the former Sinaloa cartel leader known as El Chapo, indicated in court papers that he planned to plead guilty in July to a sprawling charge known as a continuing criminal enterprise.

It was not to be.

Minutes later, a group of protesters in the back of the Capitol Hill hearing room began shouting at lawmakers to “keep your greedy hands off our Medicaid.”

They drowned out the chairman’s calls for order, and Capitol Police officers ultimately removed five people — three in wheelchairs — as the dozens of lawmakers on the panel looked on. (The Capitol Police later said that officers had arrested 26 people for illegally protesting inside a congressional building.)

The disruptions were a raucous kickoff to a meeting that was expected to go all night and well into Wednesday — one committee member estimated it could take as long as 28 hours — as Republicans and Democrats sparred over the plan, a key part of major legislation to enact President Trump’s domestic agenda.

It unfolded as the tax-writing House Ways and Means Committee met to consider a $2.5 trillion tax proposal that would extend Mr. Trump’s 2017 tax cuts; temporarily fulfill his campaign pledges not to tax tips or overtime pay; roll back subsidies for clean energy; and create a new type of tax-advantaged investment account for children. A third panel, the House Agriculture Committee, was to meet Tuesday night to begin considering another piece of the bill that would slash nutrition assistance to help raise money for the plan.

But the bulk of the drama on Tuesday was at the Energy and Commerce Committee. During the first hour alone, Republicans giving opening statements were interrupted repeatedly by protesters who accused them of taking health care away from vulnerable people. G.O.P. lawmakers, in turn, accused Democrats of misrepresenting the Medicaid cuts they are proposing to score political points.

Mr. Guthrie labored to keep control over the proceedings, at one point presiding over a shouting match over whether members of his panel were allowed to use the word “lying” in their remarks. (Republicans had been permitted to say that Democrats were lying about the scope of the Medicaid cuts, but Democrats were barred from saying that Mr. Trump was lying about his desire to protect the program. An informal agreement to simply avoid using the word “lie” altogether for the remainder of the session fell apart a few hours later.)

Even some Democratic senators came to take in the spectacle. Senators Cory Booker of New Jersey, Brian Schatz of Hawaii and Tina Smith of Minnesota were on hand.

All before lawmakers had debated a single provision of the measure.

The bill’s proposed reductions in Medicaid coverage and its expansion under the Affordable Care Act have become a flashpoint for Democrats and an area of concern for vulnerable Republicans who are wary of the political consequences of supporting cuts to insurance programs that have become popular with Americans.

Though House Republicans shied away from a huge structural overhaul of Medicaid, their proposal would reduce federal spending by an estimated $912 billion and cause 8.6 million people to become uninsured, according to a partial analysis from the Congressional Budget Office that was circulated by Democrats on the committee. Around $700 billion in cuts would come from changes to Medicaid and the Affordable Care Act.

Republicans argued that their proposed cuts would help control rising Medicaid costs by targeting “waste, fraud and abuse” and ensuring the program’s long-term health.

“Medicaid was created to protect health care for Americans who otherwise could not support themselves, but Democrats expanded the program far beyond this core mission,” Mr. Guthrie said.

Their proposal calls for stricter paperwork requirements across the program, makes changes that affect federal funding to states and adds a work requirement to Medicaid that requires poor, childless adults to prove they are working 80 hours every month to stay enrolled.

That provision, which targets an expansion of Medicaid under the Affordable Care Act, would not kick in until January 2029, after the next presidential election.

During their opening remarks, Democrats on the committee held up matching posters with photographs of constituents they deemed the “faces of Medicaid.” The lawmakers told their stories as a way of humanizing people who rely on the program.

Representative Debbie Dingell of Michigan directly addressed a family who had traveled to Washington in the hearing, who she said needed Medicaid to care for a child with Down syndrome. Representative Marc Veasey of Texas held his phone up to the microphone, inviting a constituent to speak about how Medicaid affected her. Mr. Guthrie ruled that out of order.

Some of the people being highlighted were not at risk of losing coverage under the Republican proposal. And Democrats frequently claimed that the Republican plan would cause 13.7 million Americans to become uninsured, inflating the bill’s effects on coverage by about five million people.

Pointing to these discrepancies, Republican lawmakers accused Democrats of dishonest politicking.

“Not a single person on these posters is going to be affected,” Representative Kat Cammack of Florida said.

“It’s unfortunate that people are so enraged by misinformation,” Representative Gary Palmer, Republican of Alabama, said, referring to a woman who was taken from the room by the police after she shouted that she was H.I.V. positive and that the Medicaid cuts “will kill me.”

The hallway outside the committee’s hearing was packed with protesters, many of them wearing shirts or bearing signs that read “Hands Off Medicaid.” Others wore shirts reading “Fight for Planned Parenthood.” The organization is targeted by a provision in the bill that would block Medicaid from funding health providers that also offer abortion services.

“Hopefully, everyone understands that these demonstrations — people feel very strongly,” Representative Frank Pallone Jr., the top Democrat on the committee, said. “Because they know they’re losing their health care.”

Margot Sanger-Katz contributed reporting.

“We’ve come to a screeching halt because we’re 100 percent dependent on this money to do this work,” said James Antaki, a biomedical engineering professor leading the research. Unless the funding is restored within the next few months, he said, the project will be “cast to the four winds.”

The withdrawal of a $6.5 million grant, just a ripple in a wave of deep Trump administration funding cuts for research universities over allegations of antisemitism, has little to with the program’s scientific merit.

The White House said it paused the financing because the administration is pursuing a civil rights investigation into Cornell for its handling of pro-Palestinian student protests, and it noted funding could be resumed in the future. The program is among more than 140 research programs at Cornell that have received stop-work orders and grant termination notices, the university said.

Professor Antaki said he has been working on the pump for three decades, but with the current four-year grant, his team had been aiming to receive Food and Drug Administration approval for a clinical trial by 2029. If that trial were successful, he said, the pump would be widely available by 2030.

The pump, about the size of a tube of lip balm, is a golden device of titanium, copper and magnets with a bladed cylinder that spins at 14,000 revolutions per minute. It is intended to support the flow of blood from the child’s heart for up to a year while the child is awaiting a heart transplant or surgery, Professor Antaki said.

The pump, called the PediaFlow, would fill a desperate need for babies and children with congenital heart conditions, researchers said. For those children, the only option at present is a cumbersome mechanical device called the Berlin Heart, which can produce adverse side effects, including strokes. That device is in short supply.

Last month, the Trump administration froze more than $1 billion in funding for Cornell, $790 million for Northwestern and $2 billion for Harvard, according to U.S. officials, as it pursued civil rights investigations into the schools over allegations of antisemitism and racism.

A stop-work order sent to Professor Antaki, dated April 8, did not say why the government was withdrawing funding. “Your organization may not resume work under this agreement nor incur costs or expenses,” it said.

The Defense Department, which sent the stop-work order, deferred comment to its Military Health System, which said Monday that it was looking into the matter but did not comment further.

The development of the device relies on government funding because there is not a large enough market to support commercial research, said Harvey Borovetz, a bioengineering professor at the University of Pittsburgh who is working with the Cornell team on the pediatric heart-pump project.

“It’s not that people don’t like children,” said Professor Borovetz, but there are “orders of magnitude fewer potential patients in the pediatric realm, at least today, than in the adult world, and so of course the companies are going to focus on the adult market.”

The decision by Judge Haines, who was nominated by President Trump during his first term, cut against recent rulings by three other federal judges — in Texas, Colorado and New York — all of whom had determined that the administration was using the Alien Enemies Act unlawfully.

Those judges found that Mr. Trump’s proclamation invoking the act improperly stretched its meaning, ruling that mass migration — even by people who may be members of Tren de Aragua — does not constitute an “invasion” or “predatory incursion,” as the act requires. Judge Haines is the first to find that Mr. Trump’s proclamation under the act was legal.

The American Civil Liberties Union, which has taken the lead in challenging deportations under the Alien Enemies Act, said it would appeal Judge Haines’s decision.

The Supreme Court agreed in early April to temporarily allow the administration to proceed with its use of the law, provided it gave migrants the opportunity to challenge their deportations in court. As a result, judges around the country have been considering a series of challenges from migrants potentially subject to deportation under the law, including about 10 brought by the A.C.L.U.

One of those challenges has returned to the Supreme Court, where a ruling related to a group of Texas detainees could come any time.

Like some of her colleagues, Judge Haines found that the administration had not given detainees held under the Alien Enemies Act sufficient due process, as required by the Supreme Court. But her finding that Mr. Trump’s proclamation under the act was legal increases pressure on the Supreme Court to resolve issues surrounding the president’s use of the 18th-century statute.

“We disagree with the ruling and will appeal because the Alien Enemies Act is a wartime measure that cannot be used during peacetime to address migration or criminal activity,” said Lee Gelernt, a lawyer for the A.C.L.U. “But we are pleased that the court rejected the government’s argument that they can remove people in a mere 12 hours.”

Mr. Gelernt said that “at the appropriate time,” he also planned to contest the government’s claim that his client, known by the initials A.S.R., was in fact a member of Tren de Aragua. The government has used an eight-point scale that assesses tattoos and clothing to decide who is and is not deportable under Mr. Trump’s proclamation, according to court documents.

The A.C.L.U. has also brought a separate suit in Federal District Court in Washington, seeking to protect a related group of immigrants: about 140 Venezuelan men who were sent to El Salvador under the act in March and have been there ever since in the custody of jailers at a notorious prison known as CECOT.

The judge overseeing that case, James E. Boasberg, has indicated that he probably has the authority to consider the suit even though the men are no longer on U.S. soil. At a hearing last week, Judge Boasberg suggested that American officials might have what is known as “constructive custody” over the men because the Trump administration sent them to El Salvador under a deal with the Salvadoran government.

The dynamic has played out repeatedly in recent weeks as Mr. Trump backed off, to varying degrees, on his plans to transform Gaza into the “Riviera of the Middle East,” turn Canada into the 51st state and beat China into submission with tariffs.

Now, two very different tests are emerging. One is over where Mr. Trump stands, with America’s biggest allies or with President Vladimir V. Putin of Russia, on preserving Ukraine’s sovereignty and safety in any cease-fire deal. The other, with Iran, may determine whether he is really willing to stand aside and let Israel bomb Iran — or join in, despite the risks — if he cannot extract a better nuclear deal than what President Barack Obama got, and cut off Iran’s pathway to a bomb.

Both those negotiations lack the numeric symmetries of tariff negotiations. Thousands if not millions of lives are potentially at stake. Both involve decades of grievance, dating back to the Iranian revolution and the breakup of the Soviet Union.

And Russia and Iran appear to be honing their strategies after watching Mr. Trump in action. Emissaries from those countries are hinting to Mr. Trump’s negotiator, Steve Witkoff, that there may be some investment opportunities for Americans if the United States eases off its demands. Mr. Witkoff, like Mr. Trump, has a history in real estate.

China proved an interesting example of Mr. Trump taking a maximalist approach only to climb down later. And in that case, too, Beijing appeared to be watching and learning Mr. Trump’s patterns.

When Mr. Trump placed tariffs on Chinese-made goods more than a month ago, he warned Beijing’s leaders, and those of other nations on the receiving end of his “reciprocal” tariffs, “Do not retaliate.” Defiance was useless. The best deals would come for those who showed up in Washington early, with a list of concessions.

President Xi Jinping of China ignored that advice. He matched the tariffs and matched again, until the figure on China’s imports to the United States hit an eye-watering 145 percent. For five weeks, Mr. Xi followed the road toward mutually assured economic destruction. Inflation and shortages loomed. Cargo ships turned around.

It took Mr. Trump roughly 40 days to back down, agreeing to an initial 30 percent tariff — still punishingly high — with no consequential Chinese concessions other than an agreement to work things out over the next 90 days.

The climb-down was so striking that it set off a predictable market rally that has now stretched over two days, Mr. Trump’s ultimate measure of approval.

But it also clarified Washington’s goals. Ever since Mr. Trump began slapping tariffs on U.S. adversaries and allies alike, central questions have loomed: Were tariffs, in the president’s mind, a mechanism to reshape the global trading order? To force a re-industrialization of America, even to produce products it makes little sense to make in America? Or is he envisioning a new source of income intended to supplement taxes to pay for a government that for 30 years has spent far more than it takes in?

At various moments, Mr. Trump has suggested all three were at play. But it now seems evident that what really excites him is using the tariffs as a cudgel, and to make his minimum 10 percent tariff on all foreign goods look like a bargain, even if it is onerous to consumers. Everything above that number is highly negotiable.

“President Trump’s willingness to use whatever economic means necessary to bring our trading partners to the table appears to be working in the short term,” Michael B. Froman, who served as United States Trade Representative under Mr. Obama, said on Tuesday. “A slew of negotiations are underway, and concepts of a plan have been agreed to,” he said.

“The question is to what end, and at what cost?” asked Mr. Froman, now the president of the Council on Foreign Relations. “Will his negotiating tactics cause lasting damage, including making it more difficult to get partners to work with us on other important priorities, which undermines potential economic wins?”

In the case of China, Treasury Secretary Scott Bessent set some narrow goals, which sounded very much like the Biden administration’s rationale for placing export controls on chips and chip-making equipment headed for China, and to block Huawei, the Chinese telecommunications giant, from the U.S. market.

“We do not want a generalized decoupling from China,” Mr. Bessent said Monday on CNBC. “But what we do want is a decoupling for strategic necessities.”

He now has 90 days to work out what that looks like, and to see if China cracks down further on exporters of fentanyl, another effort that dates back to the Biden era.

While those talks drag into the summer — the 90-day period will expire in mid-August, unless it is extended — it seems likely that the critical moment will come in the negotiations with Russia and Iran.

Over the weekend, Mr. Trump reluctantly joined another big demand, this one against Russia. It was issued by Europe’s top leaders during a visit to Kyiv, after they called the American president and agreed on the language. It gave Russia until Monday to agree to a 30-day cease-fire.

Mr. Putin ignored the deadline, betting he would pay little price. Instead, he ordered drone attacks on Ukraine, and offered a negotiating session with Ukraine on Thursday in Istanbul. Mr. Trump leaped to endorse the idea, abandoning the condition that a cease-fire had to come first, so Ukraine was not negotiating while facing a Russian onslaught.

Mr. Trump had also offered on Monday to show up at the talks himself as he made his way home from the Middle East. But it seems unlikely Mr. Putin will be there, reducing the allure. On Tuesday, Mr. Trump said he would send Marco Rubio, now occupying dual roles as secretary of state and national security adviser, along with Mr. Witkoff and Keith Kellogg, his Ukraine adviser.

Mr. Putin clearly senses that Mr. Trump cares little about the sanctity of Ukraine’s borders or even who is responsible for the invasion. (Soon after taking office, Mr. Trump contended that Ukraine itself was responsible, contributing to the late-February blowup with President Volodymyr Zelensky in the Oval Office.)

Much of the conversation in Istanbul will focus on the control of territory that Russia now occupies, and whether Ukraine has to radically reduce its armaments, and whether NATO needs to pull back both troops and arms near Russian borders. Mr. Zelensky has vowed to attend, adding to the potential for a standoff. As Stephen Sestanovich, a Russia expert and longtime diplomat who wrote a book a decade ago entitled “Maximalist,” noted after a recent trip to Ukraine, ever since the Oval Office argument “the Ukrainians have found a way to combine gratitude with inflexibility and make it work for them.”

But in recent times, Mr. Putin, getting with the program, has dropped hints about joint Russian-American energy and mining operations, tempting a deal-hungry president to get something out of a Ukraine agreement, beyond his search for a Nobel Peace Prize. Mr. Witkoff sounded thrilled with that idea in an interview with Tucker Carlson.

Now the Iranians are trying a similar tactic.

After several weeks of conflicting statements about whether Iran could be allowed to continue enriching uranium, which can fuel a nuclear weapon, Mr. Witkoff said last week, in an interview with Breitbart, “we believe they cannot have enrichment, they cannot have centrifuges, they cannot have anything that allows them to build a weapon.”

The demands seemed pretty clear.

But the Iranians contend that Mr. Witkoff took a far more gentle approach in the negotiating room last weekend, and did not rule out allowing some nuclear activity in Iran. Meanwhile the Iranians, according to several Iranian and other officials, have begun floating ideas for nuclear energy joint ventures, perhaps with the United States, perhaps with Saudi Arabia, their regional rival. The key is all sanctions would be lifted and Iran would preserve some of the capabilities that Mr. Witkoff, and in recent days Mr. Trump, has suggested must be mothballed or dismantled.

On Tuesday in Riyadh, the Saudi capital, Mr. Trump said he was offering Iran “a new path and a much better path toward a far better and more hopeful future.” Then he said: “The time is right now for them to choose.”

But on Monday, GD Culture Group became the latest business with foreign ties to seize on Mr. Trump’s crypto venture, which channels profits directly to the Trump family and has generated conflicts of interest that have alarmed ethics experts. (Memecoins like $TRUMP are a type of cryptocurrency based on an online joke or celebrity mascot and have traditionally not had any utility beyond speculation.)

In its statement, GD Culture Group, which is traded on the Nasdaq, said it would spend $300 million on a stockpile of Bitcoin and $TRUMP, using proceeds from a stock sale to an unnamed entity in the British Virgin Islands, a popular tax haven. It confirmed that investment plan in a securities filing late Tuesday.

The purchase would create clear ethical conflicts, enriching Mr. Trump’s family at the same time that the president tries to reach a deal that would allow TikTok to keep operating in the United States rather than face a congressionally approved ban.

The announcement also shows how investors around the world, including some that have virtually no public footprint, have latched on to the president’s crypto ventures to boost their own business prospects.

Just asserting a connection to Mr. Trump’s business can quickly raise a company’s profile. GD Culture Group’s struggling stock rose 12 percent on Monday, before losing those gains the next day.

“Make no mistake. These foreign entities and governments obviously want to curry favor with the president,” said former Representative Charles Dent, a Pennsylvania Republican who was the chairman of the House Ethics Committee. “This is completely out of bounds and raises all sorts of ethical, legal and constitutional issues that must be addressed.”

Investors in foreign countries have rushed to stock up on the $TRUMP coin since it hit the market in January. Some have stated explicitly that they hoped to use their purchases to influence Mr. Trump.

GD Culture Group was less clear about its intentions. In its statement, the company said it wanted to “enhance its balance sheet with high-performance, scalable digital assets.”

It is unclear whether the company will even follow through on the announcement, or how much of the $300 million it has received from its unidentified investor. Last month, the company disclosed that it was in danger of losing its Nasdaq listing because it had failed to meet certain financial requirements.

But any purchase by GD Culture Group would be the first known example of a China-linked firm buying Mr. Trump’s memecoin. In its financial disclosures, the company has noted that its subsidiary, Shanghai Xianzhui, might be influenced by demands from the Chinese government, though that is not unusual wording for a Chinese company.

“The Chinese government may intervene or influence its operations at any time,” the company said in an annual report filed in March.

In recent weeks, the Trump family has faced an intensifying backlash in Washington over its business dealings with foreign countries.

On the Senate floor on Tuesday, Senator Christopher S. Murphy, Democrat of Connecticut, spent 20 minutes walking through the various sources of overseas money pouring into the Trump family business, including the memecoin, a real-estate deal involving the government of Qatar and a separate $2 billion crypto deal with a firm backed by the United Arab Emirates.

“If a mayor of a small town was selling meetings at City Hall for a thousand bucks, he would be run out of town on a rail, but that’s exactly what Donald Trump is doing in the Middle East and all over the world,” Mr. Murphy said.

Representatives for the White House, the Trump Organization and GD Culture Group did not respond to requests for comment.

Mr. Trump started selling the $TRUMP coin three days before his inauguration, one of several crypto ventures that he and his sons have pursued. The coin’s price briefly surged, then crashed just as quickly, costing investors billions of dollars.

Last month, Mr. Trump and his business partners announced that the top 220 buyers of the coin would be invited to a dinner with the president at his golf club in Virginia, sparking another round of frantic trading that further enriched the Trump family. An analysis by The New York Times and the crypto forensics firm Nansen found that many of the coin’s buyers were based overseas in countries including Mexico, Singapore and Australia.

Under federal law, foreign investors are barred from donating to a political campaign or a president’s inaugural fund. But Mr. Trump’s crypto ventures have offered a new avenue for these overseas buyers to support him financially.

In April, a Mexico-based shipping firm, Fr8Tech, announced that it would spend $20 million on Mr. Trump’s memecoin as a way to “advocate for fair, balanced and free trade between Mexico and the U.S.”

The statement by GD Culture Group did not mention any policy objectives. Xiaojian Wang, the chief executive, said the company was embracing “industrial transformation” through cryptocurrencies and moving to “strengthen our financial foundation.”

It was unclear how exactly GD Culture Group had secured the funding to buy hundreds of millions of dollars of crypto. In its statement, the company did not reveal any information about the entity in the British Virgin Islands that agreed to purchase its stock.

In its filing with the S.E.C. on Tuesday, GD Culture Group confirmed its plans to buy $TRUMP — but again omitted any information about the entity that is financing the purchase.

Historically, the British Virgin Islands has been a favorite jurisdiction for overseas investors seeking to maintain confidentiality, because it is easy to set up a shell company there.

Matthew Goldstein contributed reporting.

The Trump administration’s focus on white Afrikaners, an ethnic minority that ruled during apartheid, is particularly striking as it effectively bans most other refugees and targets legal and illegal immigrants alike for deportation. Those include Afghans who were granted “temporary protected status” after the disastrous U.S. withdrawal from Afghanistan in 2021, many of whom had risked their lives to help American forces.

Mr. Trump’s hard line on immigration helped propel him back to the White House as voters from both parties expressed frustration over the issue. He has promised to carry out the largest deportation operation in U.S. history, and one of the first executive orders of his second term was to suspend refugee resettlement in the United States.

But the administration’s decision to carve out an exception for white Afrikaners has raised questions about who the “right” immigrants are, in Mr. Trump’s view.

Christopher Landau, the deputy secretary of state, who greeted the Afrikaner refugees on Monday, told reporters that the group had been “carefully vetted.”

“One of the criteria was that refugees did not pose any challenge to our national security and that they could be assimilated easily into our country,” he said, without elaborating on what that meant, or why other populations would not be assimilated as easily.

Asked by a reporter to explain why people from South Africa were welcomed even as Afghans were losing their legal status in the United States, Mr. Landau suggested that the Afghans had not undergone sufficient background checks, saying that the Biden administration “had brought in people that we were not sure had been carefully vetted for national security issues.”

Tricia McLaughlin, the assistant secretary of the Department of Homeland Security, said the protections for Afghan immigrants were always meant to be temporary. Trump officials have argued that temporary protected status is being used improperly, to allow people to stay in the United States indefinitely.

“Secretary Noem made the decision to terminate T.P.S. for individuals from Afghanistan because the country’s improved security situation and its stabilizing economy no longer prevent them from returning to their home country,” Ms. McLaughlin said.

Mr. Trump has long railed against refugees, claiming that resettlement programs flood the country with undesirable people and allow criminals and terrorists into the United States.

But he has made an exception for Afrikaners, who say they have been discriminated against, denied job opportunities and have been subject to violence because of their race. Mr. Trump said on Monday that the United States had “essentially extended citizenship” to them because he said they were victims of a genocide.

There have been murders of white farmers, a focus of Afrikaner grievances, but police statistics show they are not any more vulnerable to violent crime than others in the country.

Three decades after the end of apartheid, white South Africans continue to dominate land ownership. They are also employed at much higher rates than Black South Africans and are much less likely to live in poverty.

P. Deep Gulasekaram, a professor of immigration law at the University of Colorado Law School, said the exceptions made for white Afrikaners — while other groups are kept out — “overtly advances a narrative of global persecution of whites.”

The Trump administration’s reasoning for denying Afghans temporary protected status is that Afghan migrants would not face a “serious threat to their personal safety due to an ongoing armed conflict,” Homeland Security Secretary Kristi Noem said in a statement. (Serious personal threats from “ongoing armed conflict” are among the specific criteria for temporary protected status in U.S. immigration law.)

Experts on the situation in Afghanistan questioned that reasoning, noting that security threats remain and that Afghans who cooperated with U.S. forces during America’s 20-year occupation remain at extremely high risk of imprisonment, torture or execution.

After U.S. forces left the country, Taliban officials said they would not carry out reprisals against people who had assisted American forces or the former U.S.-backed Afghan government.

But a 2023 report by the United Nations Assistance Mission in Afghanistan documented at least 800 human rights violations against former officials and armed forces members who served under the U.S.-backed government. The abuses included “extrajudicial killings, enforced disappearances, arbitrary arrests and detentions, torture and ill treatment and threats.”

Former Afghan Army members were at greatest risk, the report found, followed by national and local police officers, and people who worked in the former government’s security directorate.

“What the administration has done today is betray people who risked their lives for America, built lives here and believed in our promises,” Shawn VanDiver, president of the group AfghanEvac, said in a statement.

Nearly three decades later, President Trump has drawn accusations of corruption and self-dealing for publicly flirting with accepting a $400 million luxury jet from Qatar and promising an exclusive country club dinner and White House tour for the largest buyers of his crypto coin, one of many financial exploits enriching him and his family.

But the Republicans who control Congress aren’t rushing to convene investigative committees just yet. As is often the case when Mr. Trump’s actions or words put him squarely in the middle of a controversy, top G.O.P. lawmakers are in no hurry to question the president or amplify the criticism.

“This is a hypothetical,” the Senate majority leader, John Thune of South Dakota, said on Tuesday when asked if he was comfortable with the gifting of the jet. Should the matter move beyond the hypothetical stage, he said, “I can assure you there will be plenty of scrutiny of whatever that arrangement might look like.”

To those who were caught up years ago in the frenzy over the Lincoln Bedroom, the acceptance of Mr. Trump’s activities within his own party is discouraging to say the least.

“Where is the hue and cry?” Terry McAuliffe, a close Clinton friend and leading fund-raiser for his presidential campaigns who later became governor of Virginia, asked about Mr. Trump. “It is just astounding to me the double standard that goes on.”

At the moment, most of the criticism is coming from Democrats, such as the Senate minority leader, Chuck Schumer of New York, who said on Tuesday that he would block all Justice Department political nominees until Mr. Trump and Attorney General Pam Bondi answered questions about the jet. His move could slow the consideration of dozens of top department officials, as well as federal prosecutors and marshals.

Mr. Schumer called Mr. Trump’s suggestion that he would accept the plane “so corrupt that even Putin would give a double take,” referring to the Russian leader, Vladimir V. Putin.

“And how are Republicans responding?” he asked. “With silence.”

There has been some noise, though, from members of the G.O.P. expressing unease about the arrangement.

“If Qatar gives a plane to the president of the United States, it seems to me that raises questions of whether the administration would be in compliance with the gift law,” said Senator Susan Collins, Republican of Maine, one of the few current senators who also served at the time of the Clinton fund-raising hearings, and one of the few in her party who dares to challenge Mr. Trump.

In an interview on Fox News, Senator Rand Paul, Republican of Kentucky, said he did not “think it’s a good idea” to accept the plane, adding that there was an “appearance of impropriety.”

Senator Ted Cruz, Republican of Texas, raised national security concerns about the Qatari jet, noting the gulf nation’s backing of Hamas and Hezbollah.

“I also think the plane poses significant espionage and surveillance problems,” he told CNBC. “So we’ll see how this issue plays out — but I certainly have concerns.”

Even some of Mr. Trump’s most ardent conservative allies in the MAGA world, such as the far-right activist Laura Loomer and the podcaster Ben Shapiro, have said Mr. Trump should reconsider the gift given the donor country’s record on human rights.

Other Republicans eagerly sided with Mr. Trump, who said earlier that it would be stupid to refuse such a gift considering it would potentially save American taxpayers money.

“I’m all for it,” said Senator Tommy Tuberville, Republican of Alabama. “If they offer him a plane — the ones we got, it costs a fortune to keep going.”

Gifts and efforts to cash in on the White House have long been a touchy subject, and lesser instances have led to serious repercussions.

In a famous 1958 episode, Sherman Adams, chief of staff to President Dwight D. Eisenhower, was forced to resign after the revelation that he had accepted a vicuña overcoat and expensive rug from a New England friend with business interests before federal agencies. Mr. Eisenhower was reluctant to let him go, but go he did.

“As a result of this entire incident, all of us in America should have been made aware of one truth: this is that a gift is not necessarily a bribe,” Mr. Eisenhower told reporters.

The Clinton fund-raising investigation was prompted by revelations that some of Mr. Clinton’s significant donors had been treated to overnight stays in the revered Lincoln Bedroom and had been invited to White House coffees and golf outings. The revelations led to demands for a special counsel, though Attorney General Janet Reno refused to appoint one.

Mr. Clinton insisted he had done nothing wrong and said that while the overnight guests may have been high-powered contributors who gave millions of dollars to his campaigns, they were also his friends.

“I did not have any strangers here,” Mr. Clinton said at a February 1997 White House news conference. “The Lincoln Bedroom was never sold. That was one more false story we have had to endure, and the facts will show what the truth is.”

Senator John McCain, the Arizona Republican and later presidential candidate who was a leading proponent of tighter campaign finance rules, said that nonetheless he was disappointed in the president.

“The president of the United States, in seeking to raise money for his re-election, was willing to use the Lincoln Bedroom, probably one of the more sacrosanct places in America, in order to gain those financial funds which he felt were necessary,” Mr. McCain said.

Republicans who controlled the Senate convened months of hearings by the Governmental Affairs Committee, which in the end produced dueling Republican and Democratic findings that fund-raising activities pursued by both parties were ethically questionable, though not illegal. That report, and one by the House Oversight and Government Reform Committee, did help spur approval of Mr. McCain’s campaign finance overhaul about four years later.

Mr. McAuliffe noted that for all the claims and insinuations that swirled around the Lincoln Bedroom matter, there was never a hint that Mr. Clinton was trying to personally profit during his White House years.

By contrast, Mr. Trump’s conduct has drawn allegations of corruption since even before he began his first term, when he refused to divest from his vast business holdings when he assumed the presidency. His recent activities, including the launch of the $TRUMP memecoin that allows investors around the world to enrich him and his family, have gone much further.

“Nobody said that the Clintons in the White House enriched themselves,” Mr. McAuliffe said. “He left office broke, broke, broke.”