At least five people were killed as thousands packed into the Afghan capital's airport on Monday, rushing the tarmac and pushing onto planes in desperate attempts to flee the country after the Taliban overthrew the Western-backed government.

US soldiers fired warning shots as they struggled to manage the chaotic evacuation.

Senior US military officials said the chaos at Kabul airport left seven people dead, including some who fell from a departing American military transport jet. The officials spoke on condition of anonymity because they were not authorised to publicly discuss ongoing operations.

One witness told Reuters he had seen the bodies of five people being taken to a vehicle. Another witness said it was not clear whether the victims were killed by gunshots or in a stampede.

Meanwhile, a Pentagon official said US soldiers had killed two armed men at the airport.

“In the thousands of people who were there peacefully, two guys who had weapons brandished them menacingly. They were both killed,” the official said, insisting on anonymity.

Tolo News reported that at least 10 people were killed and several wounded in the mayhem. It said the casualties were caused both by the shots fired and a stampede that ensued.

Some of the thousands of Afghans trying to flee clung to the side of a US military plane before takeoff, in a widely shared video that captured the sense of desperation as America's 20-year war comes to a chaotic end.

Another video showed the Afghans falling as the plane gained altitude over Kabul.

Meanwhile, all commercial flights were suspended at Hamid Karzai International Airport in Kabul, according to a statement by the airport authority.

BBC reported that US troops were taking control of Kabul's international airport and the US military had secured the site. The publication added that US troops had taken over air traffic control to evacuate American and allied staff.

US troops, who are in charge of the airport, earlier fired in the air to scatter the crowd, a US official said.

Officials were not immediately available to comment on the deaths.

The Taliban swept into Kabul on Sunday after President Ashraf Ghani fled the country, bringing a stunning end to a two-decade campaign in which the US and its allies had tried to transform Afghanistan.

The country's Western-trained security forces collapsed or fled in the face of an insurgent offensive that tore through the country in just over a week, ahead of the planned withdrawal of the last US troops at the end of the month.

Massouma Tajik, a 22-year-old data analyst, described scenes of panic at the airport, where she was hoping to board an evacuation flight.

After waiting six hours, she heard shots from outside, where a crowd of men and women were trying to climb aboard a plane. She said US troops sprayed gas and fired into the air to disperse the crowds after people scaled the walls and swarmed onto the tarmac. Gunfire could be heard in the voice messages she sent to The Associated Press.

The US Embassy has been evacuated and the American flag lowered, with diplomats relocating to the airport to aid with the evacuation. Other Western countries have also closed their missions and are flying out staff and nationals.

By morning, Afghanistan's Civil Aviation Authority issued an advisory saying the civilian side of the airport had been closed until further notice and that the military controlled the airspace.

The speed of the Taliban offensive through the country appears to have stunned US officials. Just days before the insurgents entered Kabul with little if any resistance, a US military assessment predicted it could take months for the capital to fall.

Suhail Shaheen, a Taliban spokesperson, tweeted that fighters had been instructed not to enter any home without permission and to protect life, property and honour. The Taliban have also said they will stay out of the upscale diplomatic quarter housing the US Embassy complex and the posh villas of US — allied former warlords who have fled the country or gone into hiding.

US tells Taliban not to hinder evacuation

Meanwhile, a US defence official said the head of Central Command had met face-to-face with senior Taliban leaders to urge their fighters not to interfere with the US military's evacuation operations at the Kabul airport in Afghanistan.

The official said that in the meeting on Sunday in Doha, Qatar, Gen Frank McKenzie won Taliban agreement to establish a deconfliction mechanism — an arrangement by which evacuation operations at the airport can continue without interference by the new rulers of the country.

The official spoke on condition of anonymity to discuss sensitive talks not yet announced publicly.

The official said McKenzie urged the Taliban not to interfere with the evacuation and said the US military would respond forcefully to defend the airport if necessary.

Uzbekistan says 46 Afghan aircraft 'forcibly landed' in country

Also on Monday, Uzbekistan said that it forced the landing of 46 Afghan aircraft carrying 585 troops that illegally crossed its border over the weekend.

The statement from the Central Asian country's state prosecutor said 22 military planes and 24 military helicopters were “forcibly landed” at Termez airport in southern Uzbekistan on Saturday and Sunday. Among the planes that crossed the border was an Afghan military plane that crashed in the southern province of Surkhondaryo, the statement said.

The state prosecutor said that the crash came after a collision between an Afghan military plane and an Uzbek government plane that was assisting its landing.

“The pilots of these aircraft landed by parachute,” the statement said.

The prosecutor's statement also said that 158 civilians and military personnel had crossed over the Amu Darya river into Uzbekistan on Sunday and were now under criminal investigation.

Uzbekistan's neighbour Tajikistan said on Monday it had allowed over 100 Afghan military members to land at Bokhtar airport in the south of the country.

“Tajikistan received SOS signals, after which, in accordance with the country's international obligations, it was decided to allow Afghan servicemen to land at the airport,” the Tajik foreign ministry's information department told Russian news agencies Interfax and RIA Novosti.

RIA Novosti reported that three planes carrying the soldiers had landed in Bokhtar during the night.

Of the three Central Asian countries bordering Afghanistan, only Tajikistan has eschewed talks with Taliban officials, who have assured neighbours of their commitment to regional peace and infrastructure projects.