President Joe Biden warned on Saturday that another militant attack was highly likely as US troops began leaving Kabul airport after a two-week scramble by Washington and its allies to evacuate citizens and at-risk Afghans.

As Washington neared the end of its military involvement in the country with the Taliban militants it ousted 20 years ago back in power, the United States said it killed two Islamic State militants planning attacks in Afghanistan after a deadly suicide bombing outside the airport on Thursday.

American officials also warned of a high risk of additional attacks by the group - enemies of both the West and Afghanistan's new Taliban rulers - as US forces wind up their mission before a Tuesday deadline set by Biden.

The US president said the situation on the ground remained "extremely dangerous" and that military commanders had told him an attack was highly likely in the next 24 to 36 hours.

After Thursday's blast that killed scores of Afghans and 13 American troops, the most lethal incident for US service members in Afghanistan in a decade, Biden vowed to hunt down the perpetrators. He said Friday's strike was not the last.

"We will continue to hunt down any person involved in that heinous attack and make them pay," he said.

The Taliban condemned the overnight US drone strike, which took place in Nangarhar Province, an eastern area that borders Pakistan.

"The Americans should have informed us before conducting the air strike. It was a clear attack on Afghan territory," a Taliban spokesman told Reuters, adding that two women and a child were wounded in the attack.

The Taliban have said they have arrested some suspects involved in the airport blast.

Spokesman Zabihullah Mujahid also said the Taliban would take over the airport "very soon", after US forces withdraw, and announce a full cabinet in the coming days.

The Western-backed government and Afghan army melted away as the hardline Islamist militants entered the capital on Aug. 15, leaving an administrative vacuum that has bolstered fears of a financial collapse and widespread hunger.

Mujahid told Reuters the group had appointed governors and police chiefs in all but one of Afghanistan's 34 provinces and would act to solve the country's economic problems.

A US official told Reuters on Saturday there were fewer than 4,000 troops left at the airport, down from 5,800 at the peak of the evacuation mission. Pentagon spokesperson John Kirby later confirmed to reporters that the withdrawal had begun but declined to say how many service members 

The US-led invasion of Afghanistan in late 2001 overthrew the then-ruling Taliban as punishment for harboring the al Qaeda militants behind the Sept. 11 attacks that year.

The Taliban, facing the loss of billions of dollars of aid for the country, appealed to the United States and other Western nations to maintain diplomatic relations after their withdrawal; Britain said that should only happen if the Taliban allow safe passage for those who want to leave and respect human rights.

DANGEROUS FINAL DAYS

The White House said the next few days were likely to be the most dangerous of the evacuation operation. The United States and allies have taken about 113,500 people out of Afghanistan in the past two weeks, it said.

US military and allied countries' flights carried fewer people on Saturday as Washington prepared to end its mission.

With another attack against Kabul airport a near certainty, according to US officials, the State Department reiterated its warning to Americans to immediately leave the area due to "a specific, credible threat", including the South gate, new Ministry of Interior, and gate near Panjshir petrol station.

The last British flight evacuating civilians from Afghanistan left Kabul on Saturday. British troops would take small numbers of Afghan citizens with them as they leave this weekend, a defense ministry spokesperson said. Armed forces chief Nick Carter said hundreds of people who had worked with Britain would not make it through.

In the Pentagon's strike on militant suspects in Nangarhar, a US official said on Friday that an MQ-9 Reaper unmanned aircraft flown from the Middle East targeted an Islamic State militant who was planning attacks and was in a car with an associate.

Residents of Jalalabad, the provincial capital, said they had heard several explosions around midnight and community elder Malik Adib said three people were killed and four were wounded in an air strike, adding that he had been summoned by the Taliban investigating the incident.

"Women and children are among the victims," said Adib, though he did not have information about their identity.

The US military said in a statement that it knew of no civilian casualties.

While Kabul's airport has been in chaos, the rest of the city has been generally calm. The Taliban have told residents to hand over government equipment including weapons and vehicles within a week, the group's spokesman said.

The airport attack added fuel to criticism Biden faced at home and abroad for the chaos after Afghanistan's government and military collapsed before a lightning Taliban advance. He has defended his decisions, saying the United States long ago achieved its rationale for invading in 2001.