WASHINGTON >> The U.S. military reported its biggest day of evacuation flights out of Afghanistan by far today, but deadly violence that has blocked many desperate evacuees from entering Kabul’s airport persisted, and the Taliban signaled they might soon seek to shut down the evacuation.

Twenty-eight U.S. military flights ferried about 10,400 people to safety out of Taliban-held Afghanistan over the 24 hours that ended early this morning, a White House official said. The chief Pentagon spokesman, John Kirby, said the faster pace of evacuation was due in part to coordination with Taliban commanders on getting evacuees into the airport.

“Thus far, and going forward, it does require constant coordination and deconfliction with the Taliban,” Kirby said. “What we’ve seen is, this deconfliction has worked well in terms of allowing access and flow as well as reducing the overall size of the crowds just outside the airport.”

With access still difficult, the U.S. military went beyond the airport to carry out another helicopter retrieval of Americans. U.S. officials said a military helicopter picked up 16 American citizens today and brought them onto the airfield for evacuation. This was at least the second such rescue mission beyond the airport; Kirby said that last Thursday, three Army helicopters picked up 169 Americans near a hotel just beyond the airport gate and flew them onto the airfield.

President Joe Biden’s national security adviser, Jake Sullivan, said at the White House that talks with the Taliban are continuing as the administration looks for additional ways to safely move more Americans and others into the Kabul airport.

“We are in talks with the Taliban on a daily basis through both political and security channels,” he said, adding that ultimately it will be Biden’s decision alone whether to continue military-led evacuation operations beyond Aug. 31.

In a reminder of the urgency felt amid a dizzying array of security threats to the evacuation effort, the Pentagon posted a video of a laser near the airport targeting a U.S. Air Force C-17 aircraft and apparently attempting to disrupt the pilot during landing.

After more than a week of evacuations plagued by major obstacles, including Taliban forces and crushing crowds that are making approaching the airport difficult and dangerous, the number of people flown out met — and exceeded — U.S. projections for the first time. The count was more than twice the 3,900 flown out in the previous 24 hours on U.S. military planes.

Army Gen. Stephen Lyons, head of U.S. Transportation Command, which manages the military aircraft that are executing the Kabul airlift, told a Pentagon news conference that more than 200 planes are involved, including aerial refueling planes, and that arriving planes are spending less than an hour on the tarmac at Kabul before loading and taking off. He said the nonstop mission is taking a toll on aircrews.

“They’re tired,” Lyons said of the crews. “They’re probably exhausted in some cases.”

On a more positive note, Lyons said that in addition to the widely reported case of an Afghan woman giving birth aboard a U.S. evacuation aircraft, two other babies have been born in similar circumstances. He did not provide details.

The Pentagon said it has added a fourth U.S. military base, in New Jersey, to three others — in Virginia, Texas and Wisconsin — that are prepared to temporarily house arriving Afghans. Maj. Gen. Hank Williams, the Joint Staff deputy director for regional operations, told reporters there are now about 1,200 Afghans at those military bases. The four bases combined are capable of housing up to 25,000 evacuees, Kirby said.

Afghan evacuees continued to arrive at Dulles International Airport outside of Washington. A bus carried some of the latest arrivals from Dulles airport to another site for what would be one of many processing stops before they reach new homes in the United States.

Exhaustion clouded the faces of many of the adults. How does it feel to be here, a journalist asked one man. “We are safe,” he answered.

An older woman sank with relief into an offered wheelchair, and a little girl carried by an older boy shaded her eyes to look curiously around. It was an interim stop for what had been a grueling struggle over days for many to get flights out of what is now Taliban-ruled Afghanistan. The scramble to evacuate left most arrivals carrying only a bookbag or purse, or a plastic shopping bag of belongings. Some arrived for their new lives entirely empty-handed.

Biden said Sunday he would not rule out extending the evacuation beyond Aug. 31, the date he had set for completing the withdrawal of troops. And British Prime Minister Boris Johnson plans to press Biden for an extension to get out the maximum number of foreigners and Afghan allies possible. Biden is to face the U.S.’s G-7 allies in a virtual summit on Afghanistan Tuesday.

Taliban spokesman Suhail Shaheen, in an interview with Sky News, said that Aug. 31 is a “red line” the U.S. must not cross and that extending the American presence would “provoke a reaction.”

Since the Taliban seized the capital Aug. 15, completing a stunning rout of the U.S.-backed Afghan government and military, the U.S. has been carrying out the evacuation in coordination with the Taliban, who have held off on attacking under a 2020 withdrawal deal with the Trump administration.

Today’s warning signaled the Taliban could insist on shutting down the airlifts out of the Kabul airport in just over a week. Lawmakers, refugee groups, veterans’ organizations and U.S. allies have said ending the evacuation then could strand countless Afghans and foreigners still hoping for flights out.

Since Aug. 14, the U.S. has evacuated and facilitated the evacuation of about 37,000 people.

A firefight just outside the airport killed at least one Afghan soldier early today, German officials said. It was the latest in days of often-lethal turmoil outside the airport. People coming in hopes of escaping Taliban rule face sporadic gunfire, beatings by the Taliban, and crowds that have trampled many.

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