The United States is struggling to pick up the pace of American and Afghan evacuations at Kabul airport, constrained by obstacles ranging from armed Taliban checkpoints to paperwork problems. With an Aug. 31 deadline looming, tens of thousands remained to be airlifted from the chaotic country.

Taliban fighter and their checkpoints ringed the airport~major barriers for Afghans who fear that their past work with Westerners makes them prime targets for retribution. Hundreds of Afghans who lacked any papers or clearance for evacuation also congregated outside the airport, adding to the chaos that has prevented even some Afghans who do have papers and promises of flights from getting through.

It didn’t help that many of the Taliban fighters could not read the documents.

In a hopeful sign, State Department spokesman Ned Price said in Washington that 6,000 people were cleared for evacuation Thursday and were expected to board military flights in coming hours. That would mark a major increase from recent days. About 2,000 passengers were flown out on each of the past two days, Pentagon spokesman John Kirby said.

Kirby said the military has aircraft available to evacuate 5,000 to 9,000 people per day, but until Thursday far fewer designated evacuees had been able to reach, and then enter the airport.

Kirby told reporters the limiting factor has been available evacuees, not aircraft. He said efforts were underway to speed processing, including adding State Department consular officers to verify paperwork of Americans and Afghans who managed to get to the airport. Additional entry gates had been opened, he said.

And yet, at the current rate it would be difficult for the U.S. to evacuate all of the Americans and Afghans who are qualified for and seeking evacuation by Aug. 31.

President Joe Biden on Wednesday said that he will ensure no American was left behind, even if that meant staying beyond August, an arbitrary deadline that he set weeks before the Taliban climaxed a stunning military victory by taking Kabul last weekend. It was not clear if Biden might consider extending the deadline for evacuees who aren’t American citizens.

At the airport, military evacuation flights continued, but access remained difficult for many. On Thursday, Taliban militants fired into the air to try to control the crowds gathered at the airport’s blast walls. Men, women, and children fled. U.S. Navy fighter jets flew overhead, a standard military precaution but also a reminder to the Taliban that the U.S. has the firepower to respond to a combat crisis.

Of the approximately 2,000 people airlifted from the airport in the 24 hours ended Wednesday morning, nearly 300 were Americans, Kirby said. U.S. lawmakers were briefed Thursday morning that 6,741 people had been evacuated since Aug. 14, including 1,762 American citizens and Green Card holders, according to two congressional aides.