President Biden, in remarks on Friday, vowed to evacuate all Americans out of Afghanistan and defended his administration from criticisms over the withdrawal.

But in doing so, he made several misleading or false claims about the pullout and evacuation, which have been chaotic as Americans and tens of thousands of Afghan allies try to flee through the airport in Kabul.

Here’s a fact-check of the president’s remarks.

What Mr. Biden said

This is misleading. While leaders of countries allied with the United States have been hesitant to publicly criticize the withdrawal, some members of their governments have not minced words in questioning American leadership and credibility.

In Germany, the chairman of Parliament’s Foreign Relations Committee called the withdrawal “a serious and far-reaching miscalculation by the current administration” and said it did “fundamental damage to the political and moral credibility of the West.” Armin Laschet, the head of Chancellor Angela Merkel’s Conservative Party and a candidate in the election to succeed her, called it the “biggest debacle” that NATO had ever seen. Ms. Merkel also criticized it privately, according to German news media reports.

In Britain, the pullout has raised doubts among some officials about the reliability of the United States as an ally. Tom Tugendhat, a Conservative member of Parliament and the chairman of the Foreign Affairs Committee, characterized it the “biggest foreign policy disaster” since the 1956 Suez crisis, saying that “we need to think again about how we handle friends, who matters and how we defend our interests.”

Latvia’s defense minister, Artis Pabriks, said that the withdrawal caused “chaos” and showed that the West was “weaker globally.”

What Mr. Biden said

False. Al Qaeda’s presence in Afghanistan has certainly been reduced since the United States invaded, but Mr. Biden is wrong to say that the terrorist group is no longer in the country.

A United Nations Security Council report released in June estimated that Al Qaeda still had a presence in at least 15 of Afghanistan’s 34 provinces. The Defense Department’s Office of Inspector General said in a report released on Wednesday that “the Taliban continued to maintain its relationship with Al Qaeda, providing safe haven for the terrorist group in Afghanistan.”

After Mr. Biden spoke, John F. Kirby, a Pentagon spokesman, confirmed in a news conference that Al Qaeda had a presence in Afghanistan.

What Mr. Biden said

This is misleading. Reports from Afghanistan contradict this statement, and other government officials have been more cautious when describing the conditions for American citizens traveling to the airport.

The United States Embassy in Kabul sent a security alert on Wednesday warning American citizens, legal residents and their families that the “United States government cannot ensure safe passage to the Hamid Karzai International Airport.”

Asked about Mr. Biden’s claim that no American had been denied access to the airport, Ned Price, a spokesman for the State Department, said in a news conference on Friday that the department “has received only a small number of reports from American citizens that their access has been impeded in some way, that they have faced any sort of hardship or resistance, getting to the airport.”

Mr. Kirby, the Pentagon spokesman, also said in the news conference that he was aware of “sporadic reports of some Americans not being able to get through checkpoints,” but that they were able to get through “by and large.”

Politico reported that Defense Secretary Lloyd J. Austin III told Congress on Friday that some Americans trying to leave Afghanistan had been harassed and beaten by Taliban fighters.

An unnamed American resident in Afghanistan told ABC News that he had witnessed people holding U.S. passports not being allowed through Taliban checkpoints. Clarissa Ward, a CNN reporter in Kabul, said after Mr. Biden’s remarks that she had difficulty reaching the airport.

“Working how to get to this airport is like a Rubik’s Cube,” Ms. Ward said on CNN on Friday. “Anyone who says that any American can get in here is — yes, I mean, technically, it’s possible. But it’s extremely difficult, and it is dangerous.”