WASHINGTON—President Biden has delivered regular remarks about the widening U.S. evacuation efforts in Afghanistan that critics say often paint a rosier picture than the facts on the ground warrant and at times deflect blame for the rapidly deteriorating situation.

Mr. Biden has sometimes appeared to play down the difficulties facing Americans and Afghan allies trying to get to Kabul’s airport; he has glossed over domestic and international disagreements about his approach; and he has made a contested case that last week’s chaos was inevitable.

On Tuesday, as the Taliban warned they would prevent Afghans from leaving the country, Mr. Biden and his senior aides expressed optimism that the U.S. would be able to continue evacuating U.S. citizens and Afghan allies. Witnesses on the ground said the Taliban had begun blocking roads. But a Taliban official said the new policy applied only to those Afghans without documentation for foreign travel and was aimed at reducing the size of the crowd around the airport.

“There still seems to be a disconnect between assertions of massive progress in Washington and what I’m hearing from almost everybody concerned in Kabul,” said Rep. Tom Malinowski (D., N.J.).

Mr. Biden has said the buck stops with him for the situation in Afghanistan, and the White House said he had been forthright with the public on the challenges there. His advisers said he was the first president in two decades to give an honest assessment of the flaws in the U.S. approach to the war.

Afghans waited to board a U.S. military aircraft to leave Afghanistan last week at Kabul’s airport.

Photo: shakib rahmani/Agence France-Presse/Getty Images

“In a highly fluid situation on the ground, the entire administration—from the president on down—has continually updated the country with timely and accurate information on our unprecedented work to evacuate tens of thousands of people in a matter of days,” White House spokesman Michael Gwin said.

In a series of statements over the past week, Mr. Biden and his senior aides have made the case that the scenes of chaos in Kabul were inevitable. The question of inevitability has been contested by intelligence experts and officials in Afghanistan.

Mr. Biden announced the plan to withdraw all U.S. troops on April 14. The evacuation of at-risk Afghans began over three months later, on July 30.

The effort to evacuate Americans and at-risk Afghans would have been easier during this three-month interval because the Afghan government controlled access to Kabul airport and all major cities, national security analysts said.

Biden administration officials have said they didn’t begin a large-scale evacuation earlier at the request of the Afghan government, which fled without warning after the Taliban reached the outskirts of Kabul. They also blamed the Trump administration for processing visa applications too slowly.

British and Canadian troops stood guard at the airport in Kabul over the weekend as the U.S. tried to pick up the pace of evacuations.

Photo: wakil kohsar/Agence France-Presse/Getty Images

Since last week, the U.S. has relied on the Taliban to allow access to the airport. “They’re cooperating, letting American citizens get out, American personnel get out, embassies get out, et cetera,” Mr. Biden said of the Taliban in an interview with George Stephanopoulos of ABC News on Aug. 18. He added that Afghan allies were having “some difficulty” getting out of the country.

Though the U.S. is speeding up the pace of evacuations, the Taliban have threatened, blocked and sometimes beaten American, Afghan and other travelers seeking access to the airport, witnesses have said.

The president has also asserted that the U.S. is on the same page as its North Atlantic Treaty Organization allies.

“Afghanistan has been a joint effort with our NATO allies. We went in together and we’re leaving together,” Mr. Biden said at the White House on Friday.

President Biden was briefed by his national security team on Sunday in the White House Situation Room.

Photo: Erin Scott/The White House/Associated Press

While many NATO allies agree with Mr. Biden’s decision to leave Afghanistan, some of the U.S. partners in Afghanistan have called for a slower withdrawal.

European Council President Charles Michel, one of the European Union’s top two officials, said several European leaders expressed concerns about the U.S. plan to withdraw by Aug. 31 during a virtual Group of Seven leaders meeting on Tuesday. He said the Europeans called on Mr. Biden to secure the airport as long as necessary to complete the evacuations.

The White House said it has worked in lockstep with NATO on the withdrawal and pointed to the more than two dozen countries that agreed to assist in evacuation efforts as a sign of global support for the administration’s efforts.

In the ABC News interview, Mr. Biden said his top military advisers didn’t recommend that he maintain a small contingent of several thousand U.S. troops in Afghanistan. “No one said that to me that I can recall,” the president said.

Thousands crowded Kabul's airport looking for evacuation flights as President Biden stood by the looming Aug. 31 deadline for U.S. troops to withdraw from Afghanistan. The Taliban said they wouldn’t allow foreign troops past the date. Photo: Sky Exclusive The Wall Street Journal Interactive Edition

But multiple U.S. officials said the president’s top generals, including Chairman of the Joint Chiefs of Staff Army Gen. Mark Milley, urged Mr. Biden to keep a force of about 2,500 troops while seeking a peace agreement to help maintain stability. Defense Secretary Lloyd Austin said a full withdrawal wouldn’t provide insurance against instability.

Mr. Biden has argued that the U.S. military has degraded al Qaeda’s presence in Afghanistan, at one point suggesting that the group no longer exists in the country.

“What interest do we have in Afghanistan at this point with al Qaeda gone? We went to Afghanistan for the express purpose of getting rid of al Qaeda in Afghanistan, as well as getting Osama bin Laden. And we did,” Mr. Biden said during remarks at the White House on Friday.

The United Nations said in June that the group is present in at least 15 Afghan provinces. U.S. intelligence assessments say that al Qaeda could reconstitute itself within 18 months to two years after the U.S. leaves, a timeline that may be reassessed now that the Taliban are in power.

Taliban fighters at a checkpoint in Kabul on Sunday. Witnesses have reported the Taliban were threatening, blocking and sometimes beating travelers trying to reach the airport.

Photo: Rahmat Gul/Associated Press

Biden administration officials have acknowledged that al Qaeda still has a presence in Afghanistan, but said the group currently doesn’t pose a threat to the U.S. homeland.

In explaining why the U.S. didn’t get more Afghan allies out of the country before the Taliban took over, Mr. Biden and his aides have said that some Afghans didn’t want to leave in the run-up to the country’s collapse.

”I know that there are concerns about why we did not begin evacuating Afghans—civilians—sooner. Part of the answer is some of the Afghans did not want to leave earlier—still hopeful for their country,” Mr. Biden said last week. The administration hasn’t provided data to back up that assertion.

Facing threats from the Taliban, thousands of Afghan interpreters and others who aided the U.S. over the past two decades have been waiting for years to receive a visa.

“President Biden’s repeated claim that Afghan refugees don’t really want to leave is false and appalling,” said Adam Bates, a lawyer at the International Refugee Assistance Project. “This should be self-evident to anyone watching the desperate scenes from the Kabul airport.”

Thousands of Afghans who worked for the U.S. military and government and have so far been unable to obtain a special immigrant visa fear for their safety as the U.S. completes its pullout.

Photo: Paula Bronstein/Getty Images

—Siobhan Hughes and Stephanie Armour contributed to this article.

Write to Jessica Donati at jessica.donati@wsj.com and Andrew Restuccia at andrew.restuccia@wsj.com