President Biden said Tuesday that the United States intended to withdraw completely from Afghanistan at the end of the month as planned, rebuffing pleas from Britain, France and other NATO allies to keep troops in Kabul and hastening the end of a frantic evacuation that has become a grim coda to two decades of war.

Even as Mr. Biden spoke from the White House, officials said the United States had already begun to reduce its military presence at Hamid Karzai International Airport in Kabul, sending about 300 of the 5,800 Marines and soldiers home in anticipation of the conclusion of their rescue mission within a week.

“The sooner we can finish, the better,” the president said, hours after informing world leaders of his intentions during an emergency virtual meeting. Citing the threat from an Islamic State affiliate known as ISIS-K and operating in Afghanistan, he said that “every day we’re on the ground is another day we know that ISIS-K is seeking to target the airport, attack both U.S. and allied forces and innocent civilians.”

But Mr. Biden did not close the door to extending what has become an immense evacuation effort. He said that he had asked the Pentagon and the State Department for contingency plans in case it became necessary to stay longer.

“I’m determined to ensure that we complete our mission,” he said.

The president said that more than 70,000 people had been ferried out of harm’s way since Aug. 14, the day before the Taliban swept into power in Kabul; on Tuesday, the Pentagon reported its biggest number of daily evacuations from the Kabul airport so far, saying it had airlifted 21,600 people out of the country over 24 hours.

The fast-approaching American withdrawal coincided with a threat by the Taliban to stop Afghans from traveling to the airport, which crowds have mobbed for days, under pitiless sun and at risk of brutal attacks by militants. It was an ominous sign that for the thousands of people still desperate to leave, the window may already be slamming shut.

The rapidly unfolding developments came as the world leaders pledged unity in the face of the changing landscape in Afghanistan and the C.I.A. director met secretly with the Taliban’s leader. But the flurry of diplomacy failed to alter a harrowing dynamic: The Taliban are tightening their grip, the Americans are leaving and the options for countries scrambling to extract their citizens and Afghan allies are dwindling.

Even though the pace of evacuations has accelerated in recent days, the number of people airlifted out is well below the total number of Americans, foreign citizens and Afghan allies who are trying to leave the country. And the timetable for civilian evacuations is probably significantly shorter than a week.

The Pentagon spokesman, John F. Kirby, said it would take several days to remove all of the 5,800 troops who are securing Kabul’s airport, as well as their equipment. At some point in the coming days, the military’s focus will shift from evacuations to the drawdown.

As crowds continued to throng the airport, the Taliban sought to assert their authority over a country they conquered in lightning fashion. A spokesman, Zabihullah Mujahid, said Taliban militants would block Afghans from the airport for their own safety and reiterated that the United States must leave by Aug. 31.

“The road that ends at the Kabul airport has been blocked,” Mr. Mujahid said at a news conference on Tuesday. “Foreigners can go through it, but Afghans are not allowed to take the road.”

For the first time, the Taliban warned women to stay off the streets and not to go to their jobs — also ostensibly for their own safety and only as a temporary measure. It was a chilling portent of the harsh repression that the Taliban imposed on women and girls the last time they ruled Afghanistan.

“We are worried our forces, who are new and have not yet been trained very well, may mistreat women,” Mr. Mujahid said. “Until we have a new procedure, they should stay home. They won’t be counted as absent, and their salaries will be paid in their homes.”

The White House has conducted its own outreach to the Taliban, dispatching the C.I.A. director, William J. Burns, to Kabul this week for talks with the Taliban leadership, according to American officials familiar with his visit.

Mr. Burns, a longtime diplomat who conducted secret nuclear talks with Iran during the Obama administration, met on Monday with Abdul Ghani Baradar, the Taliban leader who led diplomatic negotiations in Qatar with the United States government.

It was not clear whether Mr. Burns made much headway, either on the Aug. 31 deadline or broader human rights or security issues. But in his remarks at the White House on Tuesday, the president expressed nervousness about relying on assurances from the Taliban despite the high-level diplomatic outreach.

“Thus far, the Taliban have been taking steps to work with us so we can get our people out,” he said. “But it’s a tenuous situation. We’ve already had some gun fighting break out. We run a serious risk of it breaking down, as time goes on.”

Mr. Biden also rejected calls from lawmakers in both parties, who urged some of his top officials to extend the Aug. 31 deadline during a closed-door briefing on Capitol Hill, arguing that it would not be possible to evacuate all Americans and Afghan allies by then.

“There is a broad bipartisan agreement within the United States Congress that we have to get American citizens out and we have to get our Afghan partners and allies out,” said Representative Jason Crow, Democrat of Colorado, who is a former Army Ranger. “That can’t be accomplished between now and the end of the month, so the date has to extend until we get that mission done.”

For weeks, members of Congress have been inundated with thousands of pleas from American citizens and Afghans trying to escape Afghanistan. Representative Michael McCaul of Texas, the top Republican on the Foreign Affairs Committee, said that if the president did not extend the withdrawal date, “he will have blood on his hands.”

“People are going to die, and they are going to be left behind,” Mr. McCaul said.

Mr. Biden has emphasized that he was taking the threats to the safety of Americans in Kabul seriously. In a closed-door meeting with leaders of the Group of 7 nations on Tuesday, the president told them that the danger of a terrorist attack was “very high,” according to a senior American official.

A deadly attack against American and Afghan civilians by ISIS-K would be a disaster not only for the United States, but also for the Taliban, who are moving to consolidate control over Kabul. The Taliban and the Islamic State have been enemies, fighting each other on the battlefield for control of parts of the country.

ISIS-K refers to the Islamic State’s Khorasan affiliate in Afghanistan.

Prime Minister Boris Johnson of Britain, who led the meeting, sought to put a good face on the discussions, saying the evacuation had been remarkably successful. He said leaders had agreed on a road map for dealing with the Taliban in the long term, vowing to use Afghan funds held in Western banks as a lever to pressure the Taliban.

“The No. 1 condition is that they’ve got to guarantee, right the way through to Aug. 31 and beyond, safe passage for those who want come out,” Mr. Johnson said to the BBC after the meeting.

But Mr. Johnson failed in his effort to persuade Mr. Biden to extend the evacuation beyond Aug. 31, and it was not clear what other options the allies had to protect their own citizens and Afghan allies without American military might.

Chancellor Angela Merkel of Germany said that plans were being made to find a way to ensure that “afterward we can still get as many local employees and people needing protection to be allowed to leave the country.” But her downbeat tone laid bare the sense of futility felt by Western leaders about Afghanistan.

“How can it be that the Afghan leader left the country so quickly?” Ms. Merkel said. “How can it be that Afghan soldiers who we trained for so long gave up so quickly? We will have to ask these questions, but they were not the most pressing today.”

Prime Minister Justin Trudeau of Canada, who broke away from campaigning to attend the meeting, said that Canadian troops would stay in Afghanistan to continue evacuations beyond Aug. 31 if it was necessary and possible.

“We’re going to continue to work every single day to get as many people out alongside our allies,” Mr. Trudeau told reporters in Hamilton, Ontario, before boarding a campaign bus. “The commitment by our fellow G7 nations is clear: We’re all going to work together to save as many people as possible.”

The meeting, however, came at a moment of acute strain in the trans-Atlantic alliance, with Britain and other allies bruised by what they view as the White House’s lack of consultation on the timing or tactics of the withdrawal.

Diplomats said the meeting was important to clear the air and prevent the chaotic withdrawal from undermining other joint efforts in security and counterterrorism. But it also demonstrated yet again the impotence of European allies, who acknowledged they could not stay in Kabul after the United States left.

“The withdrawal was pathetically botched but a tactical defeat doesn’t make a strategic one,” said Gérard Araud, a former French ambassador to the United States. “All the pillars of U.S. power are intact.”

Wolfgang Ischinger, a former German ambassador to Washington, said: “There is serious loss of trust, and that will require a significant reassurance effort by Washington. But the real lesson from this for Europe is this: Do we really want to be totally dependent on U.S. capabilities and decisions forever, or can Europe finally begin to be serious about becoming a credible strategic actor?”

In Taliban-controlled Kabul, the questions were more elemental. With banks closed, cash scarce, food prices rising and public services unavailable, Afghans were struggling to make sense of what life would be like under their new rulers.

Kabul’s streets were unusually quiet, in contrast to the havoc playing out at the airport. To some, however, the quiet carried its own air of menace. One man said it showed that people were hiding in their homes, “scared and terrorized.”

Reporting was contributed by Sharif Hassan, Annie Karni, Catie Edmondson, Helene Cooper, Eric Schmitt, Melissa Eddy and Ian Austen.