The Islamic State group claimed a rocket attack on Monday on the airport in Afghanistan's capital.

"The soldiers of the caliphate targeted Kabul's international airport with six... rockets," the group said in a statement.

Rockets were fired at Kabul's airport where US troops are racing to complete their withdrawal from Afghanistan and evacuate allies under the threat of Islamic State group attacks.

President Joe Biden has set a deadline of Tuesday to withdraw all US forces from Afghanistan, drawing to a close his nation's longest military conflict, which began in retaliation for the September 11 attacks.

The return of the hardline Islamist Taliban movement, which was toppled in 2001 but took back power a fortnight ago, triggered an exodus of terrified people aboard US-led evacuation flights.

Those flights, which have taken more than 122,000 people out of Kabul airport, will officially end on Tuesday when the last of the thousands of American troops pull out.

US forces are now focused chiefly on flying themselves and American diplomats out safely.

The Islamic State group, rivals of the Taliban, pose the biggest threat to the withdrawal after carrying out a suicide bomb attack at the perimeter of the airport late last week that claimed more than 100 lives, including those of 13 US troops.

Biden has warned more attacks were highly likely and the United States said it carried out an airstrike on Sunday night in Kabul on an IS-prepared car bomb.

That was followed on Monday morning by rockets being fired at the airport.

'We can't sleep'

The White House confirmed there had been a rocket attack directed at the airport, but said airlift operations there were "uninterrupted".

"The President... has reconfirmed his order that commanders redouble their efforts to prioritise doing whatever is necessary to protect our forces on the ground," the White House statement said.

An AFP photographer on Monday took images of a destroyed car with a launcher system still visible in the back seat.

A Taliban official at the scene said he believed five rockets had been fired, and all were destroyed by the airport's missile defence systems.

A suspected US drone strike had hit the car, about two kilometres from the airport.

While there were no reports of fatalities or airport damage from the rocket attacks, they caused greater anxiety for locals already traumatised by years of war.

"Since the Americans have taken control of the airport, we can't sleep properly," Abdullah, who lives near the airport and gave only one name, told AFP.

"It is either gun firing, rockets, sirens or sounds of huge planes that disturb us. And now that they are being directly targeted, it can put our lives in danger."

'Potential loss of innocent life'

The United States said the air strike on Sunday night had eliminated another threat from the Islamic State jihadists.

However, it may have also have killed civilians.

"We are aware of reports of civilian casualties following our strike on a vehicle in Kabul today," Captain Bill Urban, a US Central Command spokesman, said in a statement.

"We would be deeply saddened by any potential loss of innocent life."

In recent years, the Islamic State's Afghanistan-Pakistan chapter has been responsible for some of the deadliest attacks in those countries.

They have massacred civilians at mosques, public squares, schools, and even hospitals.

While both IS and the Taliban are hardline Sunni Islamists, they are bitter foes - with each claiming to be the true flag-bearers of jihad.

Last week's suicide bombing at the airport led to the worst single-day death toll for the US military in Afghanistan since 2011.

The IS threat has forced the US military and the Taliban to co-operate in ensuring security at the airport in a way unthinkable just weeks ago.

The Taliban have already started taking over areas vacated by US forces.

Taliban leader

The Taliban have promised a softer brand of rule compared with their first stint in power, which the US military ended because the group gave sanctuary to Al-Qaeda.

But many Afghans fear a repeat of the Taliban's brutal interpretation of Islamic law, as well as violent retribution for working with foreign militaries, Western missions or the previous US-backed government.

Western allies have warned many thousands of at-risk Afghans have not been able to get on the evacuation flights.

On Sunday, the Taliban revealed their supreme leader Hibatullah Akhundzada was in southern Afghanistan and planning to make a public appearance.

"He is present in Kandahar," said Taliban spokesman Zabihullah Mujahid, referring to his movement's spiritual birthplace.

'US exit will stop IS attacks'

The Taliban's spokesman says the hardline Islamist group will crack down on Islamic State attacks and expects them to end once foreign forces leave the country. 

"We hope that those Afghans who are influenced by IS... will give up their operations on seeing the formation of an Islamic government in the absence of foreigners," Taliban spokesman Zabihullah Mujahid told AFP in a weekend interview. 

"If they create a situation for war and continue with their operations, the Islamic government... we will deal with them," he added.

A devastating suicide bomb attack claimed by IS outside Kabul airport on Thursday killed scores of people who were hoping to flee the country, as well as 13 US service members.

Retaliatory or pre-emptive strikes by the United States on IS positions over the past few days have angered the movement, however. 

The Pentagon said it carried out a drone strike Sunday against a vehicle threatening Kabul airport that had been linked to IS.

"There is no permission for them to do such operations... our independence must be respected," he said. 

The evacuation of tens of thousands of foreigners and Afghans who feel at risk of reprisal or repression under the Taliban is due to end on Tuesday, along with the full withdrawal of US and NATO troops.

Islamic State has been highly critical of the troop withdrawal deal struck between the Taliban and Washington last year, which saw the Taliban offer security guarantees.

One IS commentary published after the fall of Kabul accused the Taliban of betraying jihadists with the US withdrawal deal and vowed to continue its fight, according to the SITE Intelligence Group, which monitors militant communications.

During the Taliban's prison break spree this summer to free its fighters, many battle-hardened IS militants were also released -- increasingly looking like a lethal error.

'Technical problems'

Although both groups are hardline Sunni Islamist militants, they have differed on the minutiae of religion and strategy, while each claiming to be the true flag-bearers of jihad.

In recent years, the IS Afghanistan-Pakistan chapter has been responsible for some of the deadliest attacks in those countries.

They have massacred civilians at mosques, public squares, schools, and even hospitals.

Mujahid reiterated that the new Taliban government will not be announced until after the last US soldier has left.

"It is important to announce the government but this requires a lot of patience. We are holding consultations to form the government responsibly," Mujahid said. 

"We have some technical problems on this issue," he added.

Banks, government offices and other public institutions remain largely shut with employees prevented from entering offices since the takeover, which sent the Afghani sliding.

The Taliban have promised to improve Afghanistan's economy, but to do that the new regime will have to rely on foreign aid - and there is no guarantee it will get the funds it needs.