WASHINGTON (Reuters) -The Taliban has told the United States it will provide safe passage for civilians to reach the airport in Afghanistan’s capital Kabul, U.S. national security adviser Jake Sullivan said on Tuesday.

Sullivan also told a White House news briefing that the United States believes the Kabul evacuation can go until Aug. 31 and it is talking to the Taliban about the exact timetable.

Thousands of U.S. troops have been flown into Kabul to assist in evacuation efforts after the collapse of Afghanistan’s military and government after swift advances by Taliban forces.

“The Taliban have informed us that they are prepared to provide the safe passage of civilians to the airport, and we intend to hold them to that commitment,” Sullivan said.

“We believe that this can go till the 31st. We are talking to them about what the exact timetable is for how this will all play out, and I don’t want to negotiate in public on working out the best modality to get the most people out in the most efficient way,” Sullivan added.

Sullivan said it is premature to say whether the United States recognizes the Taliban as the legitimate governing power in Afghanistan.

“Right now there is a chaotic situation in Kabul where we don’t even have the establishment of a governing authority,” Sullivan said. “Ultimately, it’s going to be up to the Taliban to show the rest of the world who they are and how they intend to proceed. The track record has not been good but it’s premature to address that question at this point.”

Sullivan said most people seeking to leave Afghanistan have been able to reach the airport, but the United States is addressing with the Taliban some reports of people being turned away.

“This is an hour-by-hour issue, and it’s something we’re very clear-eyed about, and very focused on holding the Taliban accountable to follow through on its execution,” he said.

Army Major General William Taylor, with the U.S. military’s Joint Staff, told a news briefing earlier on Tuesday that 4,000 U.S. troops would be at the airport by the end of the day – an increase of 1,000 – and the aim is to have one flight taking off per hour.

(Reporting by Steve Holland, Lisa Lambert, Tim Ahmann, David Brunnstrom, adnrea Shala and Daphne Psaledakis; Editing by Chris Reese and Will Dunham)