The political party on the verge of leading Austria would take an already conservative country into a growing group of nations shifting to the far-right of European politics. It has flirted with Nazi slogans, cozied up to Russia and drawn warnings from Holocaust survivors’ groups. It campaigned on promises to deport immigrants and ban political forms of Islam.

The Freedom Party, known as the FPÖ, and its firebrand leader, Herbert Kickl, were given the chance to form a governing coalition this week, after efforts to bar them from power collapsed. If they succeed in forming a government, it would be a shock to the Austrian political system and a further jolt to Western Europe, where similarly far-right parties are surging in France, Germany and elsewhere.

But it would not be a surprise.

The Freedom Party’s rise follows years of growing acceptance of the far right in Austrian politics. Its growth has been helped by scandals and an ideological shift in the more mainstream conservative party that has led Austria’s governments for 15 of the last 25 years.

Unlike in neighboring Germany, where all other parties have refused to include the right-wing-populist Alternative for Germany in federal ruling coalitions, other parties in Austria have allowed the Freedom Party to share power for years as a junior partner.

The Freedom Party has broadened its appeal in recent elections with an anti-establishment message that harshly criticizes immigrants, Covid restrictions, the European Union and support for Ukraine in its defense against the Russian invasion. The party has gained support from blue-collar workers, university graduates and, critically, women. In elections for the European Parliament this summer, it was the most popular party among Austrian voters under the age of 35.

“The idea that the FPÖ is somehow politically taboo, that train has long left the station,” said Laurenz Ennser-Jedenastik, a political scientist at the University of Vienna.

The Freedom Party was founded by former members of the SS, the Nazi paramilitary force, in the 1950s. It was largely shunned in its early years, but then slowly became part of the political establishment.

The party first entered a national government with progressive Social Democrats in 1983 and has served in four ruling coalitions since, the most recent just six years ago. It’s also active on the state level and is in coalitions in the majority of Austria’s nine states.

Until the late 1980s, the Freedom Party was a small, elitist entity largely associated with certain nationalist university fraternities. A new leader, Jörg Haider, attracted more voters by adopting campaign rhetoric harshly critical of foreigners.

That focus has become the driving force of the modern party, sharpened and intensified by Mr. Kickl, who wrote speeches for Mr. Haider early in his career. Mr. Kickl steered the party into increasingly provocative slogans, including the xenophobic “Viennese blood — too many foreigners does no one any good.”

In 2017, the Freedom Party joined a governing coalition with the conservative People’s Party. Karin Kneissl, then the Freedom Party’s choice of foreign minister, was widely criticized for dancing at her 2018 wedding with President Vladimir V. Putin of Russia. She has since moved to Russia.

The administration and the coalition collapsed quickly in a scandal involving a hidden camera, a fake Russian heiress and a former Freedom Party leader in 2019.

During the administration, Mr. Kickl served as the country’s interior minister, putting him in charge of immigration control, a subject that has been integral to the party’s platform.

He made headlines back then for suggesting “concentrating” refugees in centralized facilities. Although Mr. Kickl later claimed that he was not trying to provoke, many believe that his use of a Nazi-era phrase referencing concentration camps was deliberate.

It was also not isolated. Mr. Kickl’s party has since repeatedly invoked the term “Volkskanzler” — “the people’s chancellor” — that was used by Hitler.

While others in the party have wanted to soften the anti-immigrant rhetoric, Mr. Kickl has capitalized on raw, emotional appeals to native-born Austrian workers. He tapped into discontent over an influx of refugees to Austria from the Middle East and, later, Ukraine. At the height of the Covid-19 pandemic, he rallied opposition to vaccine mandates, lockdowns and masks.

In last fall’s campaign, Mr. Kickl promised to build “Fortress Austria” — by resorting to strict border control measures, the forced deportation of immigrants and a suspension of asylum rights for refugees, which would require breaking from a European Union agreement on migration. He called for a reversal of measures meant to fight climate change and a renewed focus on fossil fuels.

He has also pushed for political changes that some analysts say would push Austria toward a more authoritarian model of government, akin to Viktor Orban in Hungary. Those changes include new referendum procedures that would allow a relatively small slice of the electorate to force a national vote to overturn the government or dismiss individual ministers.

Mr. Kickl’s platform appealed to many voters, with the party winning the most seats in the September election for the national assembly. “There’s more demand for a certain toughness from politics,” said Christoph Hofinger, an Austrian election researcher.

For some, it caused alarm. After the election, Christoph Heubner, the executive vice president for the International Auschwitz Committee, said that for Holocaust survivors, the victory had added “a new alarming chapter to their fears and concerns.”

The Freedom Party has benefited, in part, from the problems of the People’s Party. The group won the chancellorship handily in 2017, after turning toward the right on many issues. But the People’s Party quickly fell into a series of scandals, including one related to rigged opinion polls published in the press. It also faced voter discontent over inflation and Covid restrictions, along with its most recent coalition partner, the Green Party.

After the election loss, Karl Nehammer, the incumbent chancellor from the People’s Party, said he would not enter into a coalition with Mr. Kickl. Many saw the promise, made during the campaign, as a play to hold on to the chancellery, rather than an ideological stance, since the two parties have a long history of working together in state and federal governments.

“There was never any fundamental criticism of the FPÖ’s understanding of democracy or the rule of law” from the conservatives, Mr. Ennser-Jedenastik said.

Despite months of trying, the People’s Party was unable to form a coalition without the far right. And Mr. Nehammer announced his resignation from the chancellorship this week, paving the way for the Freedom Party to emerge on top in a coalition.

In a governing coalition, Mr. Kickl will not be able to deliver on all of his promises. The next Austrian government will need to close a budget deficit, which could hamper his economic agenda, including tax cuts and social spending increases.

But the party’s popularity will give him a strong voice as he pushes for policy changes directed at foreigners and refugees, according to analysts. Likely among them: cutting social services to those who don’t speak German or reducing financial aid for refugees.

During the fall election, 29 percent of Austrians voted for the Freedom Party. Current polling now puts voter support at more than 35 percent.

“If Kickl ever feels like the other side is not taking these talks seriously, he just gets up from the table and forces early elections,” said Mr. Hofinger.

Rescuers working in subzero conditions and bracing winds searched the rubble on Wednesday after a strong quake in Tibet toppled thousands of houses in a remote area near the northern foothills of Mount Everest. Tens of thousands of residents were being transferred to safety while dozens were being treated for injuries.

At least 126 people have died and 188 were injured in the quake, which struck on Tuesday morning in Dingri County, near one of Tibet’s most historic cities, in western China, state media reported. The quake was China’s deadliest since December 2023, when 151 people were killed in a magnitude 6.2 temblor in the northwestern provinces of Gansu and Qinghai.

The area has since recorded more than 600 aftershocks, some exceeding a magnitude of 4.0, Chinese state media said. Survivors and rescuers have had to brave freezing temperatures, as the mercury dropped to a low of minus 18 degrees Celsius or 0 Fahrenheit at night. Recent aerial images near the epicenter showed frozen lake surfaces, and temperatures are expected to remain low for the next three days, which could narrow the window for rescuing survivors.

The true extent of the damage was hard to determine independently. Tibet is one of the most inaccessible and underdeveloped parts of China. Security has been heightened for decades because of tensions between Beijing and Tibetans, many of whom have struggled to maintain their cultural identity and religious traditions in a country dominated by Han Chinese. Foreign journalists are forbidden from traveling independently in the region.

Much of the relief effort is focused on warding off the cold. The state broadcaster showed video footage of rescuers setting up tents draped with an insulated layer and rigging them with light panels powered by generators as displaced residents draped in blankets huddled on cots and chairs.

Zhang Guoqing, the vice premier, visited hospitals and tent camps on Monday night. He instructed rescue teams to focus on finding remaining survivors, delivering medical care for the infirm, and ensuring that the displaced have enough food and warmth to survive the frigid winter.

Rescuers have pulled out more than 400 survivors from the rubble overnight. About 46,000 people were relocated to safety.

Chinese state media reported that road obstructions have been cleared, and electricity has resumed in most surrounding towns and villages. The state broadcaster showed footage of soldiers digging through rubble with gloved hands and shovels.

Li You contributed research in Beijing.

Lebanon’s deeply divided Parliament is set Thursday to try to elect a new president, potentially ending a yearslong political vacuum and ushering in a degree of stability for a country reeling from its bloodiest war in decades.

For more than two years, the tiny Mediterranean nation has been paralyzed by political gridlock and led by a weak caretaker government through a series of upheavals, including a historic economic collapse, a destructive war between Israel and the Lebanese militant group Hezbollah and the collapse of the Assad regime in neighboring Syria.

Lebanon’s election of a president would be the first step in forming a full-fledged government with a mandate to steady the country. But, despite the urgency, it remains unclear whether anyone will be elected at all.

The country’s Parliament is fractured along sectarian lines and lawmakers have failed in 12 previous votes to elect a new president since October 2022, when Michel Aoun stepped down from the office at the end of his six-year term.

The vote on Thursday could be no different. Lebanon is facing diplomatic pressure by the United States and other foreign donors who have hinged postwar financial support on the election of a president. But it is not clear that the leading candidate, Joseph Aoun, the U.S.-backed commander of the Lebanese military (and unrelated to the former president), will receive enough votes to be elected.

“This election is about Lebanon basically reaching a necessary milestone in its much-needed recovery,” said Lina Khatib, an associate fellow at Chatham House, a London-based research organization. “However, the reality is that Lebanon’s various political stakeholders are nowhere near reaching the consensus needed to agree on who will be the next president — even in this very critical period.”

“The stakes are higher than ever,” said Ms. Khatib.

The 14-month war between Israel and Hezbollah has left swathes of the country in ruin with little money to finance reconstruction. The World Bank estimates that the war has cost $8.5 billion in damages alone. Lebanon’s security situation also remains volatile, and the government that eventually takes shape will need to steer the country through a fragile 60-day cease-fire that diplomats hope will become permanent.

For over two years, Lebanon’s stalemate has paralyzed state institutions and exacerbated the country’s already crippling economic malaise. Hezbollah, the dominant political force in Lebanon, has long been considered one of the main stumbling blocks by many in the country. The group scuttled a bid last year to elect a top International Monetary Fund official as Lebanon’s president by walking out of the vote.

But analysts say that Israel’s lightning offensive against Hezbollah, which decimated the group’s leadership and shattered its image as a behemoth holding sway over the country, may provide the window of opportunity needed to break Lebanon’s political gridlock.

In the run-up to the coming election, Hezbollah appears to be showing some signs of flexibility, although it remains to be seen how the vote will play out. On Sunday, a senior official in the group, Wafiq Safa, signaled that it would not veto Mr. Aoun’s candidacy as many feared.

“They have calculated that they are still powerful, but they will have to make some concessions,” said Paul Salem, the vice president for international engagement at the Middle East Institute in Washington. “Now, they need massive and large-scale foreign aid, and they also need a legitimate state within which to exist — within which to protect themselves.”

“The first building block is to elect a president,” said Mr. Salem.

The Lebanese Parliament’s 128 members elect a president via a secret ballot, a process marred in recent years by walkouts. In the first round, a two-thirds majority is required, an outcome that analysts have called unlikely for Thursday. In subsequent rounds, however, a simple majority will suffice.

If a president is elected on Thursday, he would then appoint a prime minister, in consultation with Parliament, who will be tasked with forming the government. That is likely to be a long process, and the resulting executive body will ultimately be left with the herculean task of reviving the crisis-hit nation.

The Parliament speaker, Nabih Berri, a key Hezbollah ally, said in an interview with local media last week that he was determined to elect a president on Thursday. He has pledged to keep voting open until a candidate is agreed upon.

Mr. Berri conceded however that there was not yet any consensus on who that candidate would be, marking a departure from previous elections where stakeholders normally reach an informal agreement before the vote itself.

Amid the mounting uncertainty, Lebanon’s prime minister, Najib Mikati, who has become the beleaguered face of the country’s caretaker government, struck an optimistic tone on Wednesday.

“Today, and for the first time since the presidential vacancy, I feel happy,” he said in a statement. “God willing, tomorrow we will have a new president of the republic.”

Cecilia Sala, an Italian journalist who was detained last month in Iran while on a reporting trip, was released on Wednesday and is now back in Italy.

Ms. Sala, who had a journalist visa, was arrested on Dec. 19 on charges of violating the laws of the Islamic Republic of Iran, but officials there have not provided any further details of accusations against her.

The Italian government announced Wednesday morning that Ms. Sala’s release was “thanks to intense work on diplomatic and intelligence channels.”

Ms. Sala, 29, had been held for 20 days and had told her family that she was kept in an isolation cell, with only two blankets and constant light, her family has said.

On Wednesday Ms. Sala’s partner, Daniele Raineri, said she had called him and told him, “I am free.”

“I am so happy,” Mr. Raineri said as he prepared to go to the airport to greet Ms. Sala. He said the wait was “excruciating” but that Italy had done “exceptional work.”

It was unclear how Italy obtained the release of Ms. Sala.

She was taken into custody three days after the police in Milan arrested Mohammad Abedini Najafabadi, a 38-year-old Iranian, on behalf of the United States. Mr. Abedini was accused by the United States of providing drone components to Iran’s Islamic Revolutionary Guards Corps — the country’s primary military force.

The Iranian authorities said on Dec. 25 that they expected “the Italian government to prevent the violation of the human rights of the Iranian citizen who has been unjustly accused by the United States.”

Iran has often jailed foreigners and dual nationals to extract concessions from their countries, including prisoner swaps, but Iranian officials said on Monday that there had been no connection between Mr. Abedini’s arrest and Ms. Sala’s.

On Wednesday, Mr. Abedini’s lawyer in Italy, Alfredo De Francesco, said he was happy about Ms. Sala’s release and now needed to focus on his client’s case. He did not respond to questions about developments on Mr. Abedini’s case.

Ms. Sala’s visit to Iran was her first since 2021, and since then, much had changed in the country. A new president had been elected, its shadow war with Israel had moved into the open, and Bashar al-Assad, the president of Syria and a longtime ally, had recently been ousted.

Ms. Sala, a writer and podcaster, set out to document the shifting atmosphere. She interviewed a standup comedian, and she photographed women in cafes and on the streets who were not wearing head scarves, posting a selection of images on Instagram last month and describing them as “Tehran’s new faces and new streets.”

The news of Ms. Sala’s detention became public about a week later, on Dec. 27, after she received a visit from Italy’s ambassador to Iran. The detention of Ms. Sala dominated media coverage in Italy, and President Sergio Mattarella mentioned her case in his end of year message.

On Wednesday morning, Prime Minister Giorgia Meloni of Italy called Ms. Sala’s parents to tell them that she was returning, according to a government statement.

Leily Nikounazar contributed reporting.

Ukraine attacked an oil depot near a critical military airfield in southern Russia on Wednesday, the Ukrainian military said, the latest strike in a campaign to inflict pain deep inside the country even as Kyiv’s forces are losing ground at home on the battlefield.

The military said it had struck the Kristall oil storage facility in Engels, around 300 miles from the border between the two countries. It said the depot supplied fuel to the Engels airfield, which it has said is a staging ground for Russia’s long-running attacks on Ukrainian energy infrastructure, and which hosts some of Russia’s long-range, nuclear-capable bombers.

A Russian official wrote on the Telegram messaging app that a “massive” drone attack had targeted Engels. Roman Busargin, the governor of the Saratov region, said that air defenses had intercepted the drones but that falling debris had hit an “industrial facility” and ignited a fire. No one was hurt, Mr. Busargin wrote.

A video circulating on Telegram and verified by The New York Times showed several structures on fire at the Kristall facility, which is roughly five miles from the Engels airfield. Other videos verified by The Times showed what appeared to be multiple explosions and huge plumes of smoke rising into the sky.

Kyiv has repeatedly targeted the airfield in trying to limit the strikes on Ukraine’s energy system, which have plunged cities into darkness, battering the Ukrainian grid and forcing officials to scramble for alternative power options.

The latest attack came as Ukrainian forces are pressing what appears to be a renewed offensive in the Kursk region in western Russia. Both sides have reported fierce fighting over the past few days in Kursk, where Ukrainian troops seized about 500 square miles of territory in a surprise cross-border incursion last summer.

Russia has since regained roughly half of the territory it lost. Analysts have said the renewed offensive appears to be Ukraine’s attempt to regain momentum and project strength before President-elect Donald J. Trump’s inauguration.

Mr. Trump has vowed to bring the war to a quick end, without saying how. That has spurred concerns his administration might cut off military aid to Ukraine. The Biden administration has been rushing to get additional assistance to Kyiv before Mr. Trump takes the oath of office on Jan. 20.

On Wednesday, Defense Secretary Lloyd J. Austin III was traveling to Germany for a meeting on Thursday with a coalition of allies he convened to discuss Ukraine’s security needs after Russia’s full-scale invasion in 2022. It will be Mr. Austin’s 25th — and last — meeting with the group, which includes about 50 countries.

The meeting “will focus on the need to ensure continued delivery of key capabilities including air defense systems, artillery munitions, and armored vehicles,” according to the Pentagon.

When asked by reporters on Wednesday whether there was concern about the future of the coalition once Mr. Trump takes office, Pentagon officials said they were confident European allies would carry on the work — regardless of whether the new U.S. administration decreases its support.

While the scale of the new Kursk offensive remains unclear, military analysts have suggested that it could also be an attempt to force Russia to divert troops away from the front lines of eastern Ukraine, where they have been steadily wearing down Kyiv’s defenses to seize new ground.

On Monday, Russia’s defense ministry said its forces had captured Kurakhove, a strategic town in eastern Ukraine, after months of heavy fighting.

Sanjana Varghese contributed reporting.

Christian Ulloriaq Jeppesen remembers how this all started.

In 2019, during Donald J. Trump’s first term as president, Mr. Trump floated the idea of the United States buying the island of Greenland. At the time, most people in Greenland (and Denmark, the European country that controls it) thought his suggestion was a joke.

“Everyone said, ‘Ha-ha, you can’t just buy a country, he doesn’t mean it,’” Mr. Jeppesen, a native Greenlander and a radio producer, said by telephone. “Obviously that was the wrong way to take it. Look at where we are today.”

Now Mr. Trump has doubled down on his insistence that the United States needs to annex Greenland for security reasons. And that has Greenlanders asking the same questions as everyone else, but with a lot more urgency.

Is Mr. Trump just being bombastic again, floating a fanciful annexation plan that he may know is a stretch?

Or is he serious?

Based on his comments in the last few weeks, Mr. Trump appears completely serious. Never mind that Denmark’s leadership has said the territory is not for sale, and its future must be determined by the local population.

“For purposes of national security and freedom throughout the World, the United States of America feels that the ownership and control of Greenland is an absolute necessity,” Mr. Trump wrote in late December in a social media post announcing his choice for ambassador to Denmark.

At a news conference on Tuesday, the president-elect took an even more surprising swerve. He refused to rule out using military force to get Greenland. And that same day Donald Trump Jr., suddenly showed up on the island.

The president-elect’s son landed Tuesday afternoon in Greenland’s capital, Nuuk, toured some sights like a statue of an 18th-century Danish-Norwegian missionary and was hosted by a Danish Trump supporter. He said the reason for the trip was personal, not official, but the president-elect posted about his son and “various representatives” visiting and said “MAKE GREENLAND GREAT AGAIN.”

“This is all getting scary,” Mr. Jeppesen said.

At 836,000 square miles, Greenland is the world’s largest island, about a fourth the size of the United States. It elects two representatives to Denmark’s Parliament and 31 to its own, which is responsible for most aspects of the island’s government, though Denmark retains control in a few policy areas, including defense and elements of international affairs.

Its location and landscape make it desirable to Mr. Trump on several levels.

It is strategically positioned at the top of the world, east of Canada along the Arctic Sea, and home to a large American military base. It is loaded with mineral resources such as cobalt, copper and nickel.

And as climate change melts the ice, it is opening up new paths through the Arctic Sea, which is becoming a fiercely contested region for shipping, energy and other natural resources, as well as military maneuvering.

Greenland could also find itself in the middle of a cross-Atlantic showdown over its sovereignty. On Wednesday, the French foreign minister, Jean-Noël Barrot, said that Europe could not allow a nation to attack its sovereign borders — while adding that he did not expect the United States to invade Greenland.

The blast of attention falls on Greenland at a touchy time, with the local independence movement growing. Many Greenlanders feel increasingly resentful toward Denmark, which has played an overseer role for decades. For its size, Greenland has a tiny population and most of the 56,000 Greenlanders are Inuit, part of a group of peoples who also live in Canada and Alaska.

The Greenlandic language is completely different from Danish. Many people follow a culture and belief system quite apart from those in Western Europe. And, like Indigenous people in the United States and elsewhere, they have been oppressed for a long time.

The Greenlanders’ disaffection with Denmark was heightened two years ago with revelations about Danish doctors fitting thousands of Indigenous women and girls with intrauterine contraceptive devices in the 1960s and 1970s, often without their knowledge.

Danish officials have repeatedly said that Greenland is not for sale, though they have emphasized their desire for warm relations with the United States. Last month, Denmark’s king jumped into the fray by abruptly changing the country’s coat of arms to more prominently feature symbols of Greenland and the Faroe Islands (another territory under Denmark’s control) — a polar bear and a sheep.

Amid this debate over identity, many people are now puzzling over Mr. Trump’s intentions.

“Is it just a distraction?” asked Ulrik Pram Gad, a senior researcher at the Danish Institute for International Studies. “Or is it threat-based diplomacy?”

According to an agreement in 2009 that granted Greenland expanded self-rule, Greenlanders have the right to hold a referendum on independence. The reason it has happened yet, analysts say, is because Greenland is still heavily dependent on Denmark for many professional services — including doctors, nurses and teachers — as well as half a billion dollars a year in subsidies.

Aaja Chemnitz, one of the two representatives from Greenland in the Danish Parliament, said she worries that Mr. Trump is trying to pump up Greenland’s independence movement to further his own interests. In that case, she said, “We risk becoming a pawn in a game between Denmark and the US.”

Greenland benefits from the Danish welfare system, she said, and it would do a lot worse if it became part of the United States.

“I’ve seen the American system,” Ms. Chemnitz, who lived in New York while working for the United Nations, said in a telephone interview. “I know how harmful it can be for equality.”

Mr. Jeppesen, the radio producer, said Mr. Trump may also be misinterpreting the independent nature of Greenlanders. Greenland is not just a chunk of land. It is a nation, a story, a homeland.

“There is this enormous pride you get from being one of just 56,000,” Mr. Jeppesen said. “Greenland is amazing, it’s beautiful, it’s the most wonderful country in the world.”

“And it is a country fighting for independence,” he added. “Not a piece of property you can buy.”

President-elect Donald J. Trump on Tuesday refused to rule out using military force to retake the Panama Canal, which was returned by the U.S. to that country’s control decades ago.

Last month, Mr. Trump falsely accused Panama of allowing Chinese soldiers to control the vital shipping route, which connects the Atlantic and Pacific Oceans, and of overcharging American ships.

He has also claimed Panama charges U.S. vessels “exorbitant prices,” and warned that if they are not reduced after he takes office next month, he will demand that the United States be granted control of the canal “in full, quickly and without question.”

While it is unclear what prompted Mr. Trump’s recent obsession with the Panama Canal, some Republicans have long objected to a decades-old treaty that turned the shipping lane over to Panamanian control. When Ronald Reagan ran for president, he said the people of the United States were the canal’s “rightful owners” and brought audiences to their feet with the line: “We bought it; we paid for it; we built it.”

Who owns the Panama Canal?

After a failed attempt by the French to construct a canal, it was ultimately built by the United States between 1904 and 1914. And the U.S. government managed the canal for several decades.

The U.S. also played a role in the creation of the state of Panama. At the beginning of the 20th century, the isthmus of Panama was part of Colombia. When Colombia rejected a proposed canal treaty, the U.S. government encouraged a rebellion. Colombia’s northern provinces eagerly seceded, forming the Republic of Panama. The United States Navy then kept Colombian troops from suppressing the rebellion.

U.S. control of the canal created significant tensions with Panama. In 1964, anti-American riots broke out in the U.S.-controlled canal zone.

The riots led to the renegotiation of the Panama Canal treaties. In 1977, U.S. President Jimmy Carter and the Panamanian leader Omar Efraín Torrijos signed the Torrijos-Carter Treaties. The agreements guaranteed the permanent neutrality of the Panama Canal. After a period of joint custody, the treaties called for the United States to relinquish control over the canal by the year 2000.

Panama took full control in 1999, and has since operated the canal through the Panama Canal Authority.

Mr. Carter, who died on Dec. 29, always considered the treaties to be signature achievements, and they figured prominently in his obituary.

“Through a bizarre accident of timing, we now have one president fantasizing about taking back the canal at just the time the world recognizes the canal transfer as an important part of a late president’s legacy,” said James Fallows, who was Mr. Carter’s speechwriter at the time and accompanied the president on that 1978 trip to Panama.

How has Panama responded?

In a statement of rebuke to Mr. Trump last month, President José Raúl Mulino of Panama wrote “every square meter of the Panama Canal and its adjacent area belong to PANAMA.”

Mr. Mulino also said U.S. vessels are not being overcharged. Rates being charged to ships and naval vessels, he insisted, are “not on a whim.”

Panamanian officials said all countries are subject to the same fees, though they would differ based on ship size. They are established in public meetings by the Panama Canal Authority, and take into account market conditions, international competition, operating and maintenance costs, Mr. Mulino said.

Rates have gone up recently, however. That’s because starting in 2023, Panama experienced severe drought, driven by a combination of El Niño and climate change, which Mr. Trump has called a hoax. With water levels at Gatun Lake, the principal hydrological reserve for the canal, at historically low levels, authorities reduced shipping through the canal to conserve the lake’s fresh water.

A Trump spokeswoman said that because the United States is the biggest user of the canal, the increase in fees hits its ships the most.

What is China’s role in the Panama Canal?

Chinese soldiers are not, as Mr. Trump has claimed, “operating” the Panama Canal.

“There are no Chinese soldiers in the canal, for the love of God,” Mr. Mulino said in a speech Thursday. “The world is free to visit the canal.”

A Hong Kong-based firm, CK Hutchison Holdings, does manage two ports at the canal’s entrances. And some experts have said that does raise valid competitive and security concerns for the United States.

Ryan C. Berg, the director of the Americas program at the Center for Strategic and International Studies, a Washington think tank, noted that CK Hutchison would likely have data on all ships coming through the Panama Canal. China has been using its shipping and maritime operations to gather foreign intelligence and conduct espionage.

“China exercises, or could exercise, a certain element of control even absent some military conflagration,” Mr. Berg said. “I think there is reason to be worried.”

Mao Ning, a spokeswoman for the Chinese foreign ministry, said Tuesday that China “will as always respect Panama’s sovereignty” over the Panama Canal.

China is the second-largest user of the Panama Canal after the United States. In 2017, Panama cut diplomatic ties with Taiwan and recognized the island as part of China, a major win for Beijing.

Can the United States reassert control?

Not easily.

Mr. Mulino has made clear the Panama Canal is not for sale. He noted that the treaties established permanent neutrality of the canal and “guaranteeing its open and safe operation for all nations.” And the Senate ratified the Panama Canal treaties in 1978.

Mick Mulvaney, Mr. Trump’s former chief of staff, suggested that the provocations were merely part of a negotiating tactic to get rates down.

“You know, I don’t envision American troops going in to retake the canal, but you got to think that someone is out there scratching their head going, ‘Is Donald Trump crazy enough to do something like that?’” Mr. Mulvaney said Tuesday on “The Hill” on NewsNation.

Mr. Berg said the neutrality agreement made it unlikely that Panama would even be able to grant special rates to the United States. And, he noted, Mr. Mulino is “incredibly pro-American” and likely eager to help the incoming Trump administration deal with issues like illegal immigration.

“President Mulino is going to be a great ally with the United States,” Mr. Berg said. “We should not want this to devolve into some kind of political fight because we’re going to need President Mulino on a number of other issues.”

But there is, as Mr. Trump has threatened, a military option. Mr. Trump could as president order an invasion of Panama. Under the terms of its constitution, Panama has no army. But experts dismissed Mr. Trump’s threat on Tuesday as empty intimidation.

“If the U.S. wanted to flout international law and act like Vladimir Putin, the U.S. could invade Panama and recover the canal,” said Benjamin Gaden, director of the Wilson Center’s Latin America Program in Washington. “No one would see it as a legitimate act, and it would bring not only grievous damage to their image, but instability to the canal.”