Military carries out strike in Kabul as slain service members are returned to U.S.

The president spoke to the relatives of the troops, who were killed in last week's airport bombing, and participated in a "dignified transfer" - in which the remains of fallen service members are returned to the U.S. in flag-draped cases.

Thirteen U.S. troops were killed in the attack, many too young to remember a time before the war.

Earlier, the U.S. carried out a strike on a vehicle in Kabul in response to an "imminent" threat to the airport in the Afghan capital, an official said.

A U.S. military official said there were "significant secondary explosions" following the Sunday strike, indicating the presence of a "substantial amount of explosive material."

"We are confident we hit the target we were aiming for; initial reports indicate there were no civilian casualties caused by our airstrike," said the official, speaking on the condition of anonymity because of the sensitive nature of the strike.

The strike takes place as U.S. evacuation efforts are winding down with America's longest war coming to a violent end.

The Islamic State-Khorasan, or ISIS-K, the Afghanistan and Pakistan arm of the militant group, asserted responsibility for the airport attack on Thursday.

In a joint statement with nearly 100 other countries, the United States said Sunday that it had received reassurances the Taliban would permit Afghans to leave the country after the U.S. withdrawal and that Washington, along with others, would continue to take in Afghans.

"We are all committed to ensuring that our citizens, nationals and residents, employees, Afghans who have worked with us and those who are at risk can continue to travel freely to destinations outside Afghanistan," said the statement, whose signatories included the North Atlantic Treaty Organization, though notably not China and Russia.

"We have received assurances from the Taliban that all foreign nationals and any Afghan citizen with travel authorization from our countries will be allowed to proceed in a safe and orderly manner to points of departure and travel outside the country," the statement continued. "We will continue issuing travel documentation to designated Afghans, and we have the clear expectation of and commitment from the Taliban that they can travel to our respective countries. We note the public statements of the Taliban confirming this understanding."

The statement provided no further details regarding the agreement or what, if any, action would be taken if the Taliban reneges.

Secretary of State Antony Blinken told NBC's "Meet the Press" on Sunday that it was "not likely" that Washington would backtrack on its agreement to withdraw U.S. forces by Aug. 31, comments in sync with previous statements by the Biden administration.

Blinken also continued to reject criticism that the administration was caught unprepared for the Taliban's swift return to power and the subsequent need to protect Afghans who worked with the United States during its two decades in the country, and to aid Afghans who oppose the extremist group.

"Our commitment to continue to help people leave Afghanistan who want to leave and who are not out by September 1st, that endures," Blinken said. "There's no deadline on that effort. And we have ways, we have mechanisms, to help facilitate the ongoing departure of people from Afghanistan if they choose to leave."

Blinken told ABC News on Sunday that the risk of further attacks around the Kabul airport remained very high, a situation that has effectively halted most evacuation efforts.

The United States' top diplomat said there were about 300 U.S. citizens who remain in Afghanistan and want to leave.

Blinken denied the United States has given a "kill list" of American citizens and Afghan allies to the Taliban, pushing back on such allegations as "simply wrong."

"The idea that we've done anything to put at further risk those that we're trying to help leave the country is simply wrong. And the idea that we shared lists of Americans or others with the Taliban is simply wrong," Blinken said on "Meet the Press."

Elaborating, Blinken said they had in limited situations shared some names with the Taliban, which is controlling security in a loose perimeter outside Kabul airport, to assure those people could be brought into the airport. That had happened particularly in cases where people did not have the necessary credentials or documents on them, he added.

"In specific instances when you're trying to get a bus or a group of people through, and you need to show a manifest to do that … you'll share names on a list of people on the bus so they can be assured that those are people that we're looking to bring in," Blinken said. "And by definition, that's exactly what's happened."

Blinken's comments came following outrage from Republicans lawmakers, conservative commentators and others after Politico reported that the United States had provided the Taliban with the names of American citizens, green-card holders and Afghan allies to ensure their exit from Afghanistan. The report led to accusations that the United States had put these Afghans in danger if they were left behind after the United States left the country.

National Security Council spokeswoman Emily Horne later told Politico that only "in limited cases" the United States has "shared information with the Taliban that has successfully facilitated evacuations from Kabul."

Blinken emphasized Sunday that the United States has promised nothing to the Taliban and that "there are very significant expectations of the Taliban going forward if they're going to have any kind of relationship with the rest of the world." However, Republican leaders, including Senate Minority Leader Mitch McConnell, R-Ky., have scoffed at the idea that the U.S. has any leverage over the Taliban.

"They're not particularly concerned about international pressure," McConnell said on "Fox News Sunday." "These are barbarians who certainly are not motivated by what others may think of them, and they've got the neighboring countries that have actually been sympathetic to them."