WASHINGTON — President Biden claimed U.S. forces in Afghanistan were making “significant progress” in evacuating U.S. citizens and vulnerable Afghans and pledged to do everything he could to ensure their safe evacuation as the Taliban asserts control over the country.

“Let me be clear: Any American who wants to be home, we will get you home,” Biden said.

Asked whether his promise extended to Afghan nationals, Biden said that it did.

His comments opened the door to a potentially larger operation that could keep U.S. forces in Kabul beyond the president’s Aug. 31 deadline for the final drawdown of troops. About 6,000 U.S. troops have been deployed to Kabul’s international airport to assist in the evacuation effort, most of them arriving after the Taliban captured the city on Sunday.

Acknowledging the danger of what he called the “most difficult airlift in history,” Biden thanked the soldiers and Marines carrying it out, calling them brave. He also disclosed that U.S. forces went “over the wall” surrounding the airport to rescue 169 Americans who were struggling to get through Taliban checkpoints, raising the possibility that more such missions may be necessary.

Biden warned the Taliban that violence directed at American forces or interference with Americans attempting to reach the airport would result in a “swift and forceful” response. The president said that Taliban guards outside the airport were “letting in people with American passports” but acknowledged that Afghan nationals, many afraid of retribution for having aided the U.S. war effort, were facing difficulty getting through checkpoints.

“I cannot promise what the final outcome will be,” Biden said. “As commander in chief, I can assure you that I will mobilize every resource necessary.”

Following Biden’s remarks from the White House, administration officials painted a more dire picture.

Defense Secretary Lloyd J. Austin III, in a briefing call with lawmakers, said that Afghans and even some Americans had been assaulted by the Taliban outside the Kabul airport, according to one of those on the call.

Pentagon spokesman John Kirby confirmed that Americans and Afghans had been attacked, telling reporters the U.S. had warned the Taliban that such violence and harassment is “unacceptable” and that people must be granted free passage through the checkpoints.

“By and large, that’s happening,” Kirby said.

Biden said that 13,000 people had been flown out of Afghanistan since Aug. 14 and that the U.S. government had assisted in the evacuation of thousands more on private charter flights. He said 5,700 people were airlifted out on Thursday.

Rep. Michael McCaul of Texas, the top Republican on the House Foreign Affairs Committee, said Biden’s comments were “completely divorced from reality” and urged him to do more to rescue endangered people who are stuck outside the airport.

“We still have no strategy as to how we can get Americans to the airport who are trapped behind checkpoints in Kabul or outside of Kabul,” McCaul said in a statement.

Biden’s speech from the White House was an effort to bookend a tumultuous week with a second address on Afghanistan, focusing Americans’ attention on the effectiveness of the last-minute airlift operation. It came five days after Biden took a defiant stance in the face of bipartisan criticism over the chaos of the ongoing U.S. withdrawal once the Taliban toppled the country’s former government.

The president’s message of progress was upended by an eight-hour shutdown of the Kabul airport on Friday after Qatar, a top destination for rescue flights in recent days, informed Washington that it would not accept more planeloads of Afghan evacuees. As officials raced to address the snarl, Biden delayed his remarks by an hour, giving aides time to revise his message.

With Vice President Kamala Harris, Austin and Secretary of State Antony J. Blinken standing behind him, Biden said that flights had resumed.

Although he continued to focus on his overarching rationale for ending the 20-year war in Afghanistan, Biden was less prickly in responding to questions from reporters than he was Wednesday in an interview with ABC News’ George Stephanopoulos.

Asked about reports of an unheeded warning last month in a State Department “dissent channel,” urging the administration to ramp up its evacuations, the president said he had received “all kinds of cables ... all kinds of advice.”

In drawing down forces, Biden said, he went with the “consensus opinion” — that the Taliban wouldn’t overrun the Afghan military so quickly — and reiterated his words from Monday: “I made the decision. The buck stops with me.”

But he struggled to address the larger question of why American officials seemed ill-prepared for the swift Taliban takeover, or whether the debacle gave him pause about the accuracy of U.S. assessments of terrorism risks emerging from Afghanistan.

Biden rejected the idea that the chaotic withdrawal had hurt America’s credibility with its longtime allies, but that assertion belied public criticism from several foreign ministers, who said the U.S. had not consulted with them prior to the president’s April drawdown announcement and the last-minute evacuation effort.

Biden also expressed more empathy for the Afghans whose desperation has been clear in images of them clinging to the wheels of a departing C-17 military aircraft and facing gunfire near the airport.

“The last week has been heartbreaking,” Biden said, referencing videos showing Afghans acting “out of sheer desperation.”

“I don’t think any one of us can see those pictures,” he said, “and not feel that pain on a human level.”