KABUL, Afghanistan -- US President Joe Biden on Monday defended the withdrawal of American troops from Afghanistan, even in the face of the Taliban's stunning victory, which prompted panic in Kabul with thousands mobbing the airport in a desperate attempt to flee.

In his address at the White House -- his first public appearance since the Islamist insurgents took control of the country in astonishing fashion at the weekend -- he admitted the Taliban advance had unfolded more quickly than expected.

And he did not shy away from heaping criticism at the Western-backed government that was overthrown in Kabul, saying US troops could not defend a nation whose leaders "gave up and fled," as did President Ashraf Ghani.

"We gave them every chance to determine their own future. We could not provide them with the will to fight for that future," Biden said, adding he could no longer ask US soldiers to risk their lives in the country, 20 years on.

"The mission in Afghanistan was never supposed to be nation-building."

The Taliban captured Kabul, and many other cities, with little bloodshed -- but in the capital, a sense of panic and fear overwhelmed residents, some of whom worried about a repeat of the insurgents' brutal Islamist rule from 1996 to 2001.

At the airport, frantic Afghans tried to board the few flights available throughout the day, before US forces -- sent in to secure the facility -- were forced to temporarily shut down military and civilian operations due to the rowdy crowds.

"We are afraid to live in this city," a 25-year-old ex-soldier told AFP as he stood among huge crowds on the tarmac.

"Since I served in the army, the Taliban would definitely target me."

The United States -- which was left shocked by the rapid collapse of the Afghan government -- has sent 6,000 troops to ensure the safe evacuation of embassy staff, as well as Afghans who worked as interpreters or in other support roles.

Other governments including France, Germany and Australia also organised charter flights.

On Monday, dramatic footage posted on social media showed hundreds of men running alongside a US Air Force plane as it rolled down the runway, with some clinging to the side of it.

In other videos, civilians frantically clambered up an already overcrowded and buckling jetway.

The airport reopened in the early hours of Tuesday, a US general said, adding that US personnel were now in charge of air traffic control.

- 'Time to test and prove' -
Taliban fighters have taken over checkpoints across Kabul, and militants with rifles slung over their shoulders walked through the streets of the Green Zone, the heavily fortified district that houses most embassies and international organisations.

Ghani's departure on Sunday finalised the collapse of his government. His whereabouts are currently unknown.

The Taliban sought to reassure the international community that Afghans should not fear them, with co-founder Abdul Ghani Baradar saying the militants needed to show that they could "serve our nation and ensure security".

China was the first major nation to flag support for the Taliban, stating it was ready for "friendly relations". Both Russia and Iran also made diplomatic overtures.

The State Department said any US ties with a Taliban government would depend on their respect of human rights and rejection of extremism.

Biden issued a stern warning to the insurgents, saying any threats to US interests would be met with a "devastating" military response.

- 'Failure' -
Critics say the US reputation as a global power has been badly tarnished by the Taliban's victory, nearly 20 years after they were ousted from power by a US-led invasion over their support for Al-Qaeda.

German Chancellor Angela Merkel said the US-led NATO operation in Afghanistan "has not been as successful and has not been achieved in the way that we had planned".

Britain's Defence Secretary Ben Wallace described the Taliban takeover as a "failure of the international community", assessing that the West's intervention was a job only half-done.

The US government has insisted that its two decades of war in Afghanistan was a success, defined by quashing the Al-Qaeda threat, and that the mission had far expanded beyond its original goals.

Biden said he was "left again to ask of those who argue that we should stay: how many more generations of America's daughters and sons would you have me send to Afghanistan's civil war?"

The United Nations Security Council said Monday the international community must ensure Afghanistan does not become a breeding ground for terrorism under the Taliban, following an emergency meeting in New York.

"The following days will be pivotal," UN Secretary-General Antonio Guterres said. "The world is watching. We cannot and must not abandon the people of Afghanistan."