The tens of thousands of Afghans desperate to flee the Taliban now face a harrowing dilemma: Where to go?

After the last American evacuation planes departed from Kabul on Monday, the Taliban spokesman Zabihullah Mujahid said that the Afghan capital’s airport would reopen for air traffic within days. He also tried to assuage fears of retribution, saying that Afghans with passports and visas would be allowed to leave the country, regardless of their role during the American occupation.

But with the airport’s future uncertain and evacuation flights no longer an option, some Afghans are scrambling for neighboring borders. Hundreds gather each day at Torkham, a major border crossing with Pakistan, hopeful that Pakistani officials will let them pass.

The United Nations refugee agency recently warned that as many as half a million Afghans could flee by the end of the year, and urged countries in the region to keep their borders open for those seeking refuge.

Filippo Grandi, the U.N. high commissioner for refugees, has estimated that about 3.5 million people have already been displaced by violence within Afghanistan.

“Most have no regular channels through which to seek safety,” he said this week, warning of an intensifying humanitarian crisis.

For those Afghans seeking to escape to Pakistan, however, there is a serious hurdle. Pakistan has said that it will not accept any more refugees from Afghanistan. Border officials only allow Pakistani citizens to cross, and the few Afghans who have a visa.

Standing on the Afghanistan side of the border at Torkham, about 140 miles east of Kabul, some families in recent days have been huddling with their belongings, determined to flee the Taliban’s rule. There are also laborers from neighboring Afghan provinces who want to cross to earn a livelihood amid spiraling cash and food shortages.

Last week, after a suicide bomb attack at the Kabul airport that killed scores of Afghans, large numbers of refugees — some helped by smugglers — managed to enter Pakistan through the Spin Boldak-Chaman crossing, roughly 70 miles southeast of Kandahar.

But Pakistani border officials said that Islamabad had since ordered tighter controls. While Afghan refugees living in Pakistan shuttled back and forth for decades without being asked questions, in recent years, Pakistan has made access more difficult, and built up a fence 1,600 miles long with Afghanistan.

In recent months, as the NATO-led mission in Afghanistan was collapsing, 30,000 Afghans were leaving Afghanistan every week, many through the Iranian border, according to the International Organization for Migration. Afghans have moved to the top of the list of asylum seekers seeking to make their way to Turkey, and then to Europe.

But there is a public backlash in Turkey against the migrants, while European governments want to avoid the 2015-16 migration crisis fueled by the war in Syria, which fanned far-right nationalist movements.

European Union ministers pledged on Tuesday to increase humanitarian aid for Afghanistan and its neighbors, but did not agree on amounts or on a common approach to resettling Afghan refugees.

Nevertheless, some Afghans are preparing for a new life abroad. This week, a large-scale mission at Ramstein Air Base, in Germany, was underway to help thousands of people, most of them Afghans who were evacuated in the final days of the mission in Kabul, prepare for resettlement.

Five babies have been born during the evacuation, including, a girl named Reach, aboard a C-17 aircraft that was bringing evacuees to the base.

For more than a week, Samiullah Naderi, a U.S. legal permanent resident, waited days and nights with his wife and son outside the airport in Kabul, Afghanistan, hoping to be let in so that they could leave on one of the dozens of daily flights out.

But on Monday, after being told that no more people would be allowed inside the airport gate, Mr. Naderi and his family returned to their apartment in Kabul with no clear path back to Philadelphia, where he has been living since last year.

“All flights are closed,” he said with an incredulous laugh. “I am scared.”

Mr. Naderi, 23, is among at least hundreds of U.S. citizens and potentially thousands of green card holders who are stranded in Afghanistan at the end of a 20-year war that culminated not in a reliable peace, but with a two-week military airlift that evacuated more than 123,000 people.

“The bottom line: Ninety percent of Americans in Afghanistan who wanted to leave were able to leave,” President Biden said on Tuesday. He said the U.S. government had alerted Americans 19 times since March to leave Afghanistan.

“And for those remaining Americans, there is no deadline,” he said. “We remain committed to get them out if they want to come out.”

President Vladimir V. Putin of Russia said on Wednesday that two decades of American military engagement in Afghanistan had yielded “zero” results.

“It is impossible to impose anything from the outside,” Mr. Putin told an audience of schoolchildren in the eastern city of Vladivostok. Moscow, like Beijing, has sought to use the U.S. withdrawal to paint America as a waning global superpower that cannot be trusted.

“For 20 years, American troops were present in this territory, and for 20 years they tried to civilize the people who live there,” said Mr. Putin, in remarks carried on the TV channel Russia 24.

Americans, he said, had sought “to introduce their own norms and standards of life, in the broadest sense of the word, including the political organization of society.”

“The result is some tragedies, some losses — both for those who did it, for the United States, and even more so for those people who live in Afghanistan. A zero result, if not negative,” he concluded.

Previously, after an August meeting with Chancellor Angela Merkel of Germany, Mr. Putin had said it was “not in Russia’s interest” to call the U.S. engagement in Afghanistan a failure. In a news conference, he said that “the lesson of Afghanistan” was that countries could not be forced to democratize.

Russia has its own history of intervention in Afghanistan, withdrawing in 1989 after a 10-year war waged by Soviet troops. With the U.S. withdrawal, Moscow has sought a role as a diplomatic and military power broker in the region. Unlike Western powers, Russia has kept its embassy in Kabul open, and Taliban guards now patrol there.

President Biden on Tuesday hailed what he called the “extraordinary success” of the evacuation of Kabul as he vehemently defended his decision to end America’s war in Afghanistan, just one day after the end of a two-week rescue of 125,000 people that saw the deaths of 13 service members.

Speaking from the Cross Hall at the White House, Mr. Biden said the nation owed a debt of gratitude to the troops who died in the evacuation mission.

“Thirteen heroes gave their lives,” he said in a speech in which he offered no apologies for either his decision to end the war or the way in which his administration executed that mission. “We owe them and their families a debt of gratitude we can never repay, but we should never, ever, ever forget.”

Mr. Biden appeared intent on forcefully rejecting criticism of the end of the 20-year war in Afghanistan, offering a defensive recounting of his decision-making and blaming former President Donald J. Trump for negotiating a bad deal with the Taliban that boxed Mr. Biden and his team in.

“That was the choice, the real choice between leaving or escalating,” Mr. Biden declared, his tone angry and defensive as he opened the first minutes of his remarks. “I was not going to extend this forever war.”

The president delivered his remarks almost 20 years after the United States ousted the Taliban from power in the wake of the Sept. 11 attacks, and just a day after the last American troops and diplomats departed the country, which is once again under Taliban rule.

Mr. Biden’s speech comes as White House officials are hoping to wind down a difficult episode for his presidency, and focus instead on domestic crises at hand — including the ongoing Delta variant wave of the Covid-19 pandemic and the aftermath of Hurricane Ida’s destructive path through the Gulf Coast.

The president is also expected to pivot in the days and weeks ahead toward a push in Congress next month to pass key provisions of his multi-trillion-dollar economic agenda, including major spending on infrastructure and social services.

Just a few weeks before Taliban militants strode into Kabul without a fight last month as the U.S.-backed government collapsed, the capital seemed a world away from the extremist group’s severe view of an Islamic society. As the weeks went by, however, there were gathering signs of crisis, soon to be etched in the faces of Afghans who ultimately decided they had no choice but to flee.

Tyler Hicks, a New York Times photographer, has captured the arc of the conflict in Afghanistan through at least 30 assignments since the American-led invasion in 2001. In July he traveled to Kabul, the western city of Herat and the northern city of Mazar-i-Sharif just weeks before each fell, when the anxiety about a Taliban takeover was intensifying. Following is his chronicle of those critical weeks.

In the weeks leading up to President Biden’s Aug. 31 deadline to withdraw U.S. troops from Afghanistan, a secretive and highly secure compound used by the Central Intelligence Agency became a hub for clandestine evacuations before parts of it were deliberately destroyed, an investigation by The New York Times found.

The C.I.A. had used part of the compound, called Eagle Base, to train Afghan counterterrorism units. Another section — the C.I.A.’s first detention center in Afghanistan, known as the Salt Pit — was where a U.S. government report found that the agency had carried out torture on detainees. Structures in both Eagle Base and the Salt Pit were demolished to prevent the Taliban from seizing sensitive materials.

Even as several of these planned detonations were happening, the heliport at the compound was still used to conduct covert evacuations, according to visual analysis and a former agency contractor.

The Times analyzed satellite imagery, corporate records, active-fire data and flight paths to assess how the evacuations and planned demolitions played out — and how the Taliban eventually easily gained access to the compound.