Negotiators from multiple countries were meeting in Qatar on Thursday to try to hash out a cease-fire in the Gaza Strip, in talks that have taken on added urgency amid fears that an anticipated attack by Iran and its allies on Israel could set off a broader regional conflict.

While cease-fire talks have been held on and off for months, the United States, Qatar and Egypt said last week that they were prepared to offer “a final bridging proposal” in the hopes of securing a deal that would free the remaining hostages in Gaza and alleviate the suffering of Palestinians after more than 10 months of war.

An Israeli official briefed on the negotiations said that the Israeli delegation would remain overnight in Doha, Qatar’s capital, and that the talks were expected to continue on Friday in an attempt to close substantial gaps between the two sides. A White House national security spokesman, John F. Kirby, said the United States also expected the negotiations to resume on Friday.

International pressure for a deal has been increasing for months, as the death toll in Gaza has risen. On Thursday, the Gazan Health Ministry reported that the number of dead had exceeded 40,000. The ministry’s figures do not distinguish between combatants and civilians.

The United States and its allies believe that a truce in Gaza might lower regional tensions, giving Iran and its ally in Lebanon, Hezbollah, a reason to reconsider — or at least temper — their anticipated strikes on Israel. Iran has vowed to retaliate for the killing in Iran just over two weeks ago of Hamas’s political leader, Ismail Haniyeh, and Hezbollah has vowed to avenge the killing hours earlier of one of the group’s top commanders in Lebanon, Fuad Shukr.

On Thursday, the Qatari prime minister, Sheikh Mohammed bin Abdulrahman Al Thani, spoke to the acting foreign minister of Iran, Ali Bagheri Kani, about the cease-fire talks and the tensions in the Middle East, “stressing the need for calm and de-escalation in the region,” according to the Qatari Foreign Ministry. An official familiar with the call described it as positive.

On Friday, the British foreign secretary, David Lammy, was scheduled to meet in Jerusalem with his French and Israeli counterparts, according to Israel’s Foreign Ministry.

“We are at a crucial moment for global stability,” Mr. Lammy said in a statement on Thursday. “The coming hours and days could define the future of the Middle East. That is why today, and every day, we are urging for our partners across the region to choose peace.”

But prospects for an immediate breakthrough appeared remote, leaving the Middle East girding for more violence. Hamas was not participating in the meeting in Doha on Thursday, with its representatives accusing Prime Minister Benjamin Netanyahu of Israel of not being genuinely interested in a cease-fire.

Mr. Netanyahu has in recent weeks toughened his country’s stance on several points, frustrating some of his own negotiators. He has said that Israel will fight in Gaza until it achieves a “total victory” over Hamas, destroying the group’s military and governing capabilities. Hamas has said it will not agree to any cease-fire that does not involve the complete withdrawal of Israeli troops from Gaza.

Although Hamas was not participating in the meeting, it has told mediators it was willing to consult with them afterward if Israel presented a serious response to its most recent counterproposal, according to two officials familiar with the talks.

The Israeli military offensive in Gaza began in response to the Hamas-led Oct. 7 assault that killed about 1,200 people in Israel; about 250 hostages were abducted and taken to Gaza. A day after Hamas struck, Hezbollah, an Iranian-backed militia in Lebanon, began attacking Israel in solidarity, and the two have traded fire since then, displacing more than 150,000 people along the Lebanese-Israeli border.

The United States has been pushing for a cease-fire for months, sending representatives to Doha and Cairo for multiple rounds of talks since President Biden’s declaration on May 31 that “it’s time for this war to end.” Mr. Biden outlined a deal then that was endorsed by the United Nations Security Council in June.

But a final agreement between Israel and Hamas has proved elusive.

Under the three-stage proposal, Hamas would gradually free the remaining hostages in Gaza in exchange for hundreds of Palestinian prisoners jailed by Israel. Israeli forces would withdraw from Gaza in phases, and both sides would negotiate the transition from a temporary truce to a permanent one.

On Thursday, Mr. Kirby, the White House spokesman, said that Egypt and Qatar were in contact with Hamas as they sought to work through the details of how to put an agreement into effect. The meeting on Thursday involved top intelligence officials from the United States, Egypt and Israel, along with the Qatari prime minister.

In Israel, relatives of the hostages were protesting in Tel Aviv on Thursday, as they sought to increase pressure on Mr. Netanyahu to reach a deal. More than 40 of the approximately 115 remaining hostages are presumed dead, according to the Israeli authorities.

“Every second there are hostages held in captivity is a severe risk to their lives,” said Jon Polin, the father of Hersh Goldberg-Polin, 23, an Israeli-American hostage, in an interview on Wednesday. Rachel Goldberg-Polin, Hersh’s mother, said it was time for everyone to agree to a “true compromise.”

“Not everyone is going to agree,” she said. “But everyone has interests and everyone gets a little bit of the interests they’re looking for. Let’s make that happen and move forward.”

Anas al-Tayeb, who lives in Jabaliya, just outside Gaza City, said many there rejoiced last month when mediators said that cease-fire talks were progressing. But just a few days later, the Israeli military again stormed neighborhoods in Gaza City.

Mr. al-Tayeb blamed both Israel and Hamas for the failure to agree to a cease-fire. He also questioned why Hamas had not accepted earlier Israeli cease-fire proposals, which broadly adhered to the three-stage framework.

“Those same conditions were offered before in previous rounds of negotiations,” Mr. al-Tayeb said. “So why didn’t they take it then?”

Vedant Patel, a State Department spokesman, said at a news conference in Washington that the broad framework for a deal had “generally been accepted” but that it was a “complicated process.”

“I don’t anticipate that coming out of the talks that there will be a deal today,” he said.

Reporting was contributed by Johnatan Reiss, Ephrat Livni and Michael D. Shear.

A day after the assassination of a senior commander of the Lebanese militant faction Hezbollah, the group vowed to retaliate against Israel. More than two weeks later, however, the response has not come as Hezbollah strikes a delicate balance between the vengeance it seeks and the risks of a backlash at home.

Lebanon is already deep in turmoil from a yearslong political and economic crisis, and its citizens are tired of strife. The country has careened from one crisis to the next since a 15-year civil war broke out in 1975. And if Hezbollah ends up in another punishing war with Israel now, the nation could well turn against it.

The Lebanese state is made up of a multitude of factions and sects and it has been controlled for years by an ineffectual caretaker government. Hezbollah, an Iran-backed Shiite Muslim group, is both part of that coalition government and considered the real power underpinning Lebanon.

As the dominant political and military force in the entire country, Hezbollah has everything to lose and knows it must tread carefully.

The group has cemented its position over the last three decades after outmaneuvering its domestic foes in a political system that divides power by sect. The group has amassed a large and potent arsenal and is more powerful than the national military. It controls or has oversight of the country’s most important infrastructure. And it has lifted up its constituents in the process, empowering, enriching and providing services to Shiites in Lebanon, a historically marginalized sect.

Many of Lebanon’s Shiites now benefit from a plethora of services run by Hezbollah, including quality health care, free education and even a boy scouts program. Meanwhile, a broken and broke Lebanese state struggles to provide even the most basic services, such as electricity, for all its citizens. And no other political party has the funds or organization to provide for their own sect as well as Hezbollah.

Hezbollah must balance its allegiances to Iran and the Palestinian cause with the tolerance, if not support, of the Lebanese people. If the group miscalculates in its retaliation, Israel has vowed a response that could devastate Lebanon again.

“Hezbollah is stuck,” said Alain Aoun, a Christian member of Lebanon’s parliament who is allied with Hezbollah. “They have to avenge the assassination of their commander, but the taste of 2006 is still in their mouths. And they know the Lebanese people cannot take it anymore.”

In 2006, Hezbollah and Israel fought a bloody, monthlong war that destroyed large swaths of southern Lebanon. Israel’s harsh response saw many Lebanese factions rally around Hezbollah. But the risk now is that many in the country may blame the militants for any further destruction rather than close ranks behind them.

Hezbollah has already been engaged in a low-level war with Israel for the last 10 months in support of Hamas, the armed Palestinian group that attacked on Israel on Oct. 7, setting off the war in Gaza. Hamas, like Hezbollah, is an Iranian ally.

Analysts say Israel and Hezbollah have carefully calibrated their attacks on each other so as not to provoke an all-out war. But there has been an ever-present danger that a single mistake or miscalculation could push one side or the other over the brink.

Those risks grew late last month when a rocket from Lebanon hit a soccer field in Majdal Shams, a Druse village in the Israeli-controlled Golan Heights, and killed 12 teenagers and children. Hezbollah denied that the rocket was its own, while U.S. and Israeli assessments concluded that it belonged to the group.

Israel retaliated in Beirut by assassinating the Hezbollah commander Fuad Shukr — a strike on the Lebanese capital seen as a potentially dangerous escalation.

That assassination came a day before a senior Hamas political leader, Ismail Haniyeh, was killed in Tehran, the Iranian capital. Iran and Hamas blamed Israel, which has not publicly taken responsibility for Mr. Haniyeh’s killing.

Western and Middle Eastern governments have been waiting anxiously to see how and when Hezbollah and Iran might retaliate while U.S. and Arab mediators redoubled efforts this week to reach an Israel-Hamas cease-fire in hopes that it would cool regional tensions.

The fear is that whatever comes next could snowball into a more intense, intractable and widespread regional war.

What matters most is not when Hezbollah will retaliate but how. Analysts say that the militants believe any attack on Israel needs to be strong enough to force Israel to rethink striking Beirut again, but not so spectacular that it provokes a devastating response against Lebanon.

“Hezbollah needs to respond in a big way to stretch Israel’s red lines but without crossing the threshold that will lead to an all-out war,” said Amal Saad, a lecturer at Cardiff University and leading Hezbollah scholar.

Any attack that kills Israeli civilians risks a potentially catastrophic counterattack on Lebanon.

Hezbollah hinted in June that it may have the intelligence and the military capabilities to penetrate deep inside Israel. It released drone footage of sensitive facilities, including an air base, in and around the city of Haifa.

Unlike Hamas in Gaza, Hezbollah has a much larger and more powerful arsenal at stake — tens of thousands of rockets and precision-guided missiles that can pummel towns and cities in Israel.

Hezbollah leader Hassan Nasrallah is well aware of the risks. Shortly after Mr. Shukr’s assassination, he addressed Israel and the world in careful language.

“I am not saying that the goal of this battle is to eliminate Israel,” Mr. Nasrallah said, softening his usual approach of calling for the annihilation of Israel, a long-term Hezbollah objective.

“The goal of this battle is to prevent Israel from winning” and from “eliminating the Palestinian resistance,” Mr. Nasrallah added, drawing a separation between the war in Gaza and Hezbollah’s support for Hamas, on the one hand, and the group’s larger, longer-running conflict with Israel.

Mr. Nasrallah said Hezbollah could retaliate separately from Iran, underscoring his group’s ability to act independently from its patron. He also said that forcing Israel to wait for a response was part of the group’s psychological warfare.

The attack that killed Mr. Shukr last month was in Dahiyeh, a Shiite neighborhood in Beirut’s southern suburbs that was flattened during the 2006 war, the last high-intensity conflict between Israel and Hezbollah. Israel also struck important national infrastructure.

Mr. Nasrallah said in 2006 that he would not have ordered the capture of two Israeli soldiers — the incident that sparked the conflict — if he had known it would lead to such a war.

In subsequent years, oil-rich Gulf nations led by Saudi Arabia spent billions of dollars to rebuild Lebanon. But if all-out war breaks out between Israel and Hezbollah now, the Gulf is unlikely to help reconstruct Lebanon on the scale it did then.

Saudi Arabia and Iran had engaged in a decades-long war of influence across the Middle East, and Lebanon was often ground zero. Iran-backed Hezbollah eventually won out against the Saudis’ Lebanese allies about a decade ago. For those reasons, robust Gulf support is unlikely this time around, even if tensions between Saudi Arabia and Iran have eased lately.

By the time the latest warfare erupted around the region, Lebanon was already severely weakened from years of political paralysis and economic decline.

Its economy collapsed in 2019, with the currency losing more than 95 percent of its value, wiping out the savings of many. That crisis precipitated a political collapse, and the caretaker government put in place at the start of 2020 was too broke to provide the most basic services to the country.

For all those reasons and more, most Lebanese do not have appetite for another big war with neighboring Israel.

In Dahiyeh last week, the usually packed Beirut suburb was eerily quiet. Normally bustling shops and streets were empty as many appeared to have fled the area, worried about a new conflict.

Sabah Suleiman was working as a seamstress next to the building Israel struck when it killed Mr. Shukr. She said she was trapped in her workshop when the strike destroyed much of the block.

Ms. Suleiman urged Hezbollah to retaliate but, at the same time, said she had deep concerns.

“I worry about my family,” she said, adding that she did not know where they would seek refuge if the conflict intensified.

Fatima, 50, lives near the Lebanese-Israeli border and said her house had been badly damaged by Israeli shelling in the past months. She recently fled for Beirut, but said she does not feel safe anywhere, fearing what a Hezbollah retaliation may bring in terms of an Israeli response.

“We are terrified,” said Fatima, who asked to be identified by her first name only so she could speak freely about Hezbollah. “Lebanon is weak economically and if we open another war, how are we going to face it? We have no water and no electricity,” she added.

“I have lost count of the retaliations. We are heartbroken. But this war is bigger than us.”

This could have been a new era for Thai democracy.

The public resoundingly ended a near-decade of military rule last year, handing an electoral mandate to a progressive party and a forceful prime minister candidate who represented none of the old power makers.

Just 15 months later, things are entirely different, and the voters had nothing to do with it. The winning party has been banned, and its candidate barred from holding office. The consensus choice who emerged then to form a government as prime minister was abruptly ousted by a top court this week.

On Friday morning, Parliament dealt the next card up, choosing Paetongtarn Shinawatra — the 37-year-old heir to a powerful and polarizing Thai political dynasty — to be the country’s new prime minister.

For many Thais, the decisions made in the past week were the latest evidence that the country is controlled by a military and royalist establishment that is bent on denying the people’s will, using the courts and the army’s presence to winnow the field.

The sudden rise of Ms. Paetongtarn has seemingly settled a period of political limbo, at least for a while. But it has added to the frustration of voters and political activists who had worked within the democratic system.

“I don’t understand what kind of games they are playing,” said Nawaphon Thoopkaew, 23, a student at Kasetsart University. “And for what?”

The selection of Ms. Paetongtarn was a result of a two-day backroom negotiation that began hours after the former prime minister, Srettha Thavisin, was ousted by the Constitutional Court on an ethics violation charge. She received 319 votes in the House of Representatives, surpassing the 247 she needed. There were no other candidates.

“I hope I can do my best to make this country go forward,” a visibly nervous Ms. Paetongtarn told reporters, adding, “my hands are shaking.”

Ms. Paetongtarn’s acceptance of the nomination surprised some observers. People close to her had previously said she was reluctant to jump into the fray. A former deputy chief executive of a family-run hotel management company, Ms. Paetongtarn’s résumé is thin for someone seeking national leadership, having played only advisory roles rather than directly governing.

But she is the daughter of Thaksin Shinawatra, the tycoon who once led the country as prime minister. After he was ousted by a military coup in 2006, his supporters battled anti-Thaksin forces in violent street protests that carried on for years. Even through the roughly 17 years he was in self-imposed exile, his political parties and his chosen candidates continued to win elections.

Ms. Paetongtarn was one of those chosen candidates in the election last year, an early front-runner for Pheu Thai. Her youth presented a possible appeal for a generation of voters that has gravitated toward the mostly young opposition.

On Thursday evening, when her nomination to become prime minister was put forward, Ms. Paetongtarn told reporters that she is close to her father, who always gives her advice.

If her main asset is that she is a Shinawatra, it is also one of her biggest troubles. Thailand’s politics are perilous, and few understand that as intimately as her family.

Her aunt, Yingluck, Thailand’s first female prime minister, was ousted in a 2014 coup and had to flee the country. Her uncle, Somchai Wongsawat, was also removed as prime minister when the Constitutional Court ordered the dissolution of his People Power Party in 2008.

Ms. Paetongtarn’s ascension means that Mr. Thaksin is again at the forefront of Thai politics, a prospect unthinkable until a few years ago. His return was in part set in motion by his rivals, beginning with last year’s victory by the Move Forward Party.

The election results stunned an establishment that saw that party, which had championed changes to a law that makes criticism of the monarchy a crime, as a dire threat. Blocking its rise required teaming up with Mr. Thaksin, whose Pheu Thai Party was the second-biggest in the winning coalition.

Pheu Thai ultimately defected and joined the conservatives. After Mr. Thaksin made a surprise return to Thailand, it was soon clear what the quid pro quo was. Although given an eight-year sentence for corruption and abuse of power, he never had to serve a day in jail.

But Mr. Thaksin has seemingly fallen out with the establishment again. In June, he was indicted on accusations of insulting the monarchy. At the same time, the case against Prime Minister Srettha, his protégé, began moving forward, ending with his ouster by the Constitutional Court on Wednesday.

Now it is Ms. Paetongtarn’s turn in the spotlight, and she will be closely scrutinized by Mr. Thaksin’s rivals and by the establishment.

For the 72 million Thais stuck in an exhausting cycle of elections, party dissolutions, protests and coups, there is a dreary sense of déjà vu.

The political upheaval has taken a toll on Thailand’s once-surging economy, now among the region’s weakest. Many of the country’s young professionals are determined to leave Thailand, in part because of the politics.

“It tells you that the Thai people’s vote doesn’t really matter, because in the span of one week, the court disenfranchised more than 14 million voters and unseated a democratically elected prime minister,” said Napon Jatusripitak, a visiting fellow with the Thailand Studies Program at Singapore’s ISEAS-Yusof Ishak Institute.

“To me, this amounts to a judicial coup that not only nullified the election results, but also establishes a very dangerous legal precedent that allows judicial institutions to intervene and check the power of future democratically elected governments for many years to come.”

But others say there is still room for optimism. One striking feature of Thailand is that despite all the repression at the top, voter and civic engagement remains high. It is home to a vibrant opposition and civil society organizations unafraid to speak up.

“The one thing that, for better or worse, is really enshrined in this system, is the idea of having elections, regardless of how seriously those elections are taken,” said Michael J. Montesano, associate senior fellow of the Thailand Studies Program at the ISEAS-Yusof Ishak Institute.

The public has not come out in the streets to protest the latest machinations, a difference from previous instances when democracy was interfered with. The Move Forward Party, which won the most votes in last year’s election and then was banned, has constantly reminded people to make their voices known at the ballot box.

The party has a successor already vowing to keep up the fight: the People’s Party. Their supporters believe that a repeated election victory for the party in three years’ time could make it harder for the establishment to repudiate the results.

Within hours of its launch last Friday, it exceeded its fund-raising target, three weeks ahead of schedule.

Kasit Piromya, a former foreign minister, points out that most of the generals and the heads of Thailand’s political parties are in their 70s, while the People’s Party is made up of people in their 30s and 40s, with new ideas and a firm ideology.

“This is the last hurrah of the establishment to retain power,” he said.

Muktita Suhartono contributed reporting.

The actors onstage reached for their pockets, each pulling out and then unfurling a Kenyan flag before a hushed crowd that packed the theater.

Then, in a solemn and chilling delivery, they began reciting the names of the dozens of people they say were killed by security forces in the monthslong mass protests that have convulsed Kenya. As they waved the flags, several members of the audience wrapped their own flags around themselves, some weeping quietly.

“The flag is no longer a cloth that flaps overhead and that is detached from the people,” Ngatia Kimathi, one of the actors in the play staged in the capital, Nairobi, said in an interview.

“The flag has become a symbol of unity and a symbol of the people’s power,” said Mr. Kimathi, who had been arrested in the protests. “In these times of death but also hope, everyone is holding onto it.”

Kenya has strict legal limits on the use of its national flag, which features two crossed spears and a shield against stripes of black, red, green and white. The law specifies that the flag is to be displayed only on government properties or on public holidays and that violators can be prosecuted. The rules were first introduced in the 1960s to limit the desecration of the flag — and a proposal to amend them several years ago never passed the Senate.

But as antigovernment protests have roiled the East African nation, protesters have embraced the flag as a symbol of solidarity against a political class they say is corrupt and has left the country with grinding poverty, skyrocketing debt, joblessness and poor infrastructure.

Activists have embraced the flag as patriotic bunting and a symbol of unity that could overcome the corrosive ethnic politics and political dynasties that have shaped Kenya for decades.

Dozens of protesters have been arrested while carrying nothing but the flag, according to lawyers, protesters and activists. While none have been charged with improper use of the flag, the lawyers said, protesters risk two months in prison or a fine of $15.

“Historically, the flag represents victory that has been gained through struggle,” said Chao Tayiana, a Kenyan historian who has begun a project collecting objects used in the protests, including flags. “So for Kenyans who envision a different future and an alternative way of living, the flag is a symbol of unity.”

The youth-led protests, which began in mid-June against proposed tax increases, have devolved into broader calls for President William Ruto to resign. At least 60 people have been killed, hundreds arrested and dozens more abducted and tortured, according to human rights groups.

In capitulating to the protesters’ demands, Mr. Ruto abandoned the tax increases and fired his cabinet. However, he reappointed many of the same, often wealthy officials, to office, further angering the protesters, who vowed to return to the streets.

“They are not listening to us,” Mr. Kimathi, the actor, said.

As they go out on the streets, protesters have advised one another on social media to carry three things: water, a phone and a flag.

Demonstrators have shown up wearing the flag as a scarf or bandanna or strapped to their belts and bags. They have draped the flag on coffins and on the bodies of dead protesters — as in the case of David Chege, who activists and rights groups say was shot by security forces in front of Parliament. They gave folded flags to the families of the deceased.

Young people, chanting “Ruto Must Go,” have also waved the flag at nightclubs, concerts and vigils. Street vendors at busy roundabouts have begun selling the flags for a few dollars. One activist has been giving away hundreds of flags before and during protests.

“My generation has been able to democratize the flag,” said Boniface Mwangi, an activist who has been at the forefront of the protests.

Growing up, Mr. Mwangi said, he was a scout member who helped raise the flag at school every Friday. He associated the flag with the then-government of the autocratic leader Daniel arap Moi and thought it was an emblem “to be feared rather than to be respected.”

When he first traveled to the United States years ago, Mr. Mwangi said, he was surprised to see the American flag everywhere. He is incensed that many Kenyan politicians affix flags to their cars so that the police would wave them through traffic jams.

Kenyan politicians, he said, had forgotten how the flag encoded the country’s history: black for the people, red for the blood spilled during the struggle for independence, green for the land and white for peace.

“The flag belongs to all of us,” said Mr. Mwangi, who was recently arrested while wearing the flag around his neck. “Now, we have liberated the flag.”

Protesters like Shakira Wafula admit they were scared when they first stepped into the street carrying the flag.

At a protest in June, Ms. Wafula was among demonstrators who engaged in a fierce running battle with the police. Hours later, exhausted, with a runny nose and burning eyes from the tear gas, she said she decided to sit down and rest at a corner near Parliament. But security forces quickly caught up with her and demanded that she leave. Ms. Wafula refused, and holding onto a metal fence, challenged the officer to move her.

Then she raised her fist in the air while holding a Kenyan flag.

The staredown with the officers went viral and was broadcast on news networks and widely shared on TikTok. Some protesters said Ms. Wafula gave them the courage to show up in the streets. A prominent artist drew a mural of her face on a wall, with the Kenyan flag next to it.

“The fear I had at the beginning that it’s illegal to be walking around with the flag in this manner is no longer there,” Ms. Wafula, a fitness instructor, said in an interview. “I permanently have a flag in my bag, and it’s making me feel connected to my country and to the other youth who are actively participating in this movement.”

For now, protesters hope the restrictive laws governing the use of the flag will be amended. Some have called for the portrait of the president, which is displayed in businesses and offices, to be replaced with the flag.

Mr. Kimathi, the actor, said he wrote poems while looking at the two flags he now owns, and thought about all those who have been killed or hurt while demonstrating for a better Kenya.

“The flag has shown us Kenyans how we can be together and fight together,” he said. “No one is above the flag.”

Russian troops are closing in on the strategic eastern Ukrainian town of Pokrovsk, according to open-source battlefield maps, casting doubts on Ukraine’s hopes that its new offensive into western Russia will prompt Moscow to scale back its attacks elsewhere on the battlefield.

After capturing several villages in the area and pushing along a railway line, Russian forces are now about eight miles from Pokrovsk, one of Ukraine’s main defensive strongholds in the Donetsk region, according to the maps, which are based on combat footage and satellite images.

The capture of the city would bring Russia a step closer to its long-held goal of seizing the entire Donetsk region, much of which it already controls. Pokrovsk, a city with a prewar population of about 60,000, sits on a key road linking several cities that form a defensive arc protecting the part of Donetsk that is still held by Ukraine.

The situation is so dire that the city’s military administration has urged residents to leave, although it has not issued a formal order. “The enemy is rapidly approaching the outskirts of Pokrovsk,” Serhii Dobriak, the head of the military administration, said on Thursday. “Evacuation is underway in the community. Don’t delay!”

Russia’s advance toward Pokrovsk is a reminder that, despite Ukrainian forces’ successful incursion into Russia’s western Kursk region, they are still losing ground on their own territory. Ukrainian soldiers on the eastern front say that the fighting there has anything but abated, and that they remain outnumbered and outgunned by Russian troops.

Military experts say that one goal of the surprise cross-border assault that Ukraine began last week in Kursk is to compel Moscow to divert troops from the front lines in Ukraine to reinforce its own border region. But so far, Russia has withdrawn only a limited number of units from the Ukrainian battlefield, instead seeking to counter attacks with less experienced combat units in Russia, analysts and United States officials say.

Ukraine’s offensive into Russia “does not affect the overall balance of the front line,” Thibault Fouillet, the deputy director of the Institute for Strategic and Defense Studies, a French research center, said in an interview. The main feature of the battlefield — Russian troops advancing slowly but steadily through bloody assaults — remained the same, he said.

Ukrainian soldiers said this week that Ukraine’s incursion into Russia had not led to a letup in Russian attacks in the Donetsk region. Serhiy Tsehotskiy, an officer with the 59th Motorized Brigade, told the Ukrainian news media on Friday that Russian forces had tried overnight to storm the town of Novohrodivka, which sits on the railroad into Pokrovsk.

“Attempts to assault and advance do not stop for a minute, and fighting continues around the clock,” he said.

President Volodymyr Zelensky of Ukraine said on Thursday that Pokrovsk and other nearby towns were “facing the most intense Russian assaults.”

The Institute for the Study of War, a Washington-based think tank that tracks battlefield developments, wrote on Thursday that “Russian forces are maintaining their relatively high offensive tempo” in the Donetsk region. In doing so, it wrote, the Russian military command was demonstrating that it “continues to prioritize advances in eastern Ukraine even as Ukraine is pressuring Russian forces” in the Kursk region.

Maps of the battlefield compiled by the institute and other independent groups show that Ukrainian troops have made marginal advances in the Kursk region over the past day, capturing at least one village and pushing into several others.

Now, however, they are facing greater resistance from reinforced Russian forces and are progressing more slowly as they try to consolidate their gains. Mr. Fouillet, the military expert, said that to hold the territory it has seized in Russia, Ukraine would have to send in more soldiers and weapons — at the risk of weakening its lines elsewhere on the battlefield.

“They’ll need to bring air defenses, install artillery, build logistic lines, replace soldiers,” Mr. Fouillet said. “Those are resources that won’t be available elsewhere.”

Soldiers fighting in the Donetsk region said they had been buoyed by the incursion into Russia. But they also said it would use up weapons and ammunition that they crucially need. One commander stationed at a hot spot on the eastern front said his brigade had fewer than four mortar guns to defend its position, and could fire only 10 shells a day per mortar.

In the fight for Pokrovsk, military analysts say that Ukrainian troops will fight hard to defend the city and prevent its capture. The city has been turned into a military garrison during the war, with many Ukrainian soldiers staying there to rest after a rotation on the front or to prepare for future operations.

Pokrovsk is also a logistical hub for the Ukrainian Army, given that it sits on a key road linking several Ukrainian-held cities in the region, including Kramatorsk, Kostiantynivka and Sloviansk. The road, Highway T054, is already within range of Russian artillery and drone strikes, but Ukraine’s army continues to use it.

Military analysts say Ukraine has prepared defensive lines of trenches and anti-armored-vehicle ditches around Pokrovsk, which could slow the advance of Russian troops. But whether these lines will ultimately hold remains to be seen.

The city’s military administration has yet to order an evacuation and has only urged residents to leave. Volodymyr Nikulin, a police officer in Pokrovsk, said that about 40,000 people were still in the city.

In recent days, officials in Pokrovsk have been touring community centers in an effort to persuade people to leave, giving them a timetable for the evacuation train and information about towns they could move to, including in the Carpathian Mountains of western Ukraine.

“The enemy is advancing at a rapid pace, and the time to pack personal belongings and leave for safer regions is running out every day,” the Pokrovsk military administration said on Thursday. “Evacuation is the only chance to save yourself and your loved ones!”