The beating blades of US military helicopters whisking American diplomats to Kabul's airport Sunday punctuated a frantic rush by thousands of other foreigners and Afghans to flee to safety as well, as a stunningly swift Taliban takeover entered the heart of Afghanistan's capital Kabul.

Two weeks from the Biden administration's planned full military withdrawal, the US was pouring thousands of fresh troops back into the country temporarily to safeguard what was gearing up to be a large-scale airlift.

Shortly before dawn Monday Kabul time, State Department spokesman Ned Price announced the US had completed the evacuation of its embassy in Afghanistan, lowering the American flag.

At the same time, the administration announced it was taking over air traffic control at Kabul's international airport, to manage the airlifts. Sporadic gunfire there Sunday frightened Afghan families fearful of Taliban rule and desperate for flights out, one of the last avenues for escape in an evacuation made far more urgent by the Taliban's weeklong sweep across the country.

NATO allies that had pulled out their forces ahead of the Biden administration's intended August 31 withdrawal deadline were sending troops back in as well this weekend to protect evacuations of their own.

Some complained the US was failing to move fast enough to bring to safety Afghans at risk of reprisal from the Taliban for past work with the Americans and other NATO forces.

"This is murder by incompetence," said US Air Force veteran Sam Lerman, struggling Sunday from his home in Woodbridge, Virginia, to find a way out for an Afghan contractor who had guarded Americans and other NATO forces at Afghanistan's Bagram air base for a decade.

Taliban forces moved early Sunday into a capital beset by fear and declared they were awaiting a peaceful surrender.

READ: Australia sends jets to fly personnel from Kabul

That arrival of the first waves of Taliban into Kabul prompted the US to begin evacuating the embassy building in full, leaving only acting ambassador Ross Wilson and a core of other diplomats operating at the airport.

Even as CH-47 helicopters shuttled American diplomats to the airport, and facing criticism at home over the administration's handling of the withdrawal, Secretary of State Antony Blinken rejected comparisons to the 1975 fall of Saigon.

A joint statement from the US State and Defense departments pledged late Sunday to fly thousands of Americans, local embassy staff and other "particularly vulnerable Afghan nationals" out of the country.

It gave no details, but high-profile Afghan women, journalists, and Afghans who have worked with Western governments and nonprofits are among those who most fear Taliban targeting for perceived Western ways or ties.

The statement promised to speed up visa processing for Afghans who used to work with American troops and officials in particular.

To many, the evacuations, and last-ditch rescue attempts by Americans and other foreigners trying to save Afghan allies, appeared far from orderly.

Hundreds or more Afghans crowded in a part of Kabul airport away from many of the evacuating Westerners. Some of them, including a man with a broken leg sitting on the ground, lined up for what was expected to be the last flight out by the country's Ariana Airlines.

US officials reported gunfire near the airport Sunday evening and for a time urged civilians to stop coming. Pentagon spokesman John Kirby said the airport was open for commercial flights – the only escape left for many ordinary Afghans – but would experience stoppages.

READ: Afghan president flees the country as Taliban move on Kabul

US C-17 transport planes were due to bring thousands of fresh American troops to the airport, then fly out again with evacuating US Embassy staffers. The Pentagon was now sending an additional 1,000 troops, bringing the total number to about 6,000, a US defence official said Sunday, speaking on condition of anonymity to discuss a deployment decision not yet announced by the Pentagon.

The Pentagon intends to have enough aircraft to fly out as many as 5,000 civilians a day, both Americans and the Afghan translators and others who worked with the US during the war.

It was by no means clear how long Kabul's deteriorating security would allow any evacuations to continue.