US anti-missile defences intercepted as many as five rockets that were fired at Kabul's airport early on Monday morning, a US official said, as the United States rushed to complete its withdrawal from Afghanistan to end its longest war.

US and allied forces are hurrying to evacuate their remaining citizens and at-risk Afghans before completing their own withdrawal by Tuesday to meet a deadline agreed between the Taliban and Washington.

The mission became more urgent and dangerous after an Islamic State suicide bomb attack on Thursday killed 13 US military personnel and scores of Afghan civilians outside the airport.

The US official, speaking on the condition of anonymity, told Reuters initial reports did not indicate any US casualties from the latest rocket attack, but that information could change.

Afghan media reports said the rocket attack was mounted from the back of a vehicle. According to Pajhwok news agency several rockets struck different parts of the Afghan capital.

The United States and allies have evacuated about 114,400 people - including foreign nationals and vulnerable Afghans - in an operation that began a day before Kabul fell to the Taliban on August 15, but tens of thousands more desperate Afghans face being left behind.

"We tried every option because our lives are in danger. They (the Americans or foreign powers) must show us a way to be saved. We should leave Afghanistan or they should provide a safe place for us," said one woman outside the airport.

Two US officials told Reuters evacuations would continue on Monday, prioritising people deemed at extreme risk. Other countries have also put in last minute requests to bring out people under that category, the officials said.

US President Joe Biden attended a ceremony on Sunday at Dover Air Force Base in Delaware to honour members of the U.S. military killed in Thursday's attack.

Biden shut his eyes and tilted his head back as the flag-draped transfer caskets carrying the remains emerged from a military plane.

None of the fallen service members was over the age of 31, and five were just 20, as old as the war in Afghanistan itself.

Biden has vowed to avenge the Islamic State attack.

A US drone strike on Sunday killed a suicide car bomber who Pentagon officials said was preparing to attack the airport on behalf of ISIS-K, a local affiliate of Islamic State that is an enemy of both the West and the Taliban.

US Central Command said it was investigating reports of civilian casualties from the strike, the second by the US military against suspected ISIS-K militants.

"We know that there were substantial and powerful subsequent explosions resulting from the destruction of the vehicle, indicating a large amount of explosive material inside that may have caused additional casualties," it said.

The departure of the last troops will mark the end of the US-led military intervention in Afghanistan, which began in late 2001, after the al Qaeda September 11 attacks on the United States.

US-backed forced ousted a Taliban government that had provided safe haven for al Qaeda leader Osama bin Laden, who was finally killed by US forces in Pakistan in 2011, and have involved in a counter-insurgency war against the Islamist militants for the past two decades.

The Taliban's 1996-2001 rule was marked by a harsh version of sharia, Islamic law, with many political rights and basic freedoms curtailed and women severely oppressed.

Taliban spokesman Zabihullah Mujahid has said the group will announce a full Cabinet in the coming days, and that the difficulties will subside quickly once the new administration is up and running.

But with its economy shattered by decades of war, Afghanistan now faces a sudden halt in inflows of billions of dollars in foreign aid.