The Taliban has taken control of parts of Kabul airport, a spokesman announced, as a 31 August deadline for the United States and its allies to complete evacuations looms.
"Today, three important locations in the military part of Kabul airport were evacuated by the Americans and are under the control of the Islamic Emirate," spokesman Bilal Karimi said on Twitter.
"Now, a very small part remains with the Americans."
Pentagon spokesman John Kirby has said the Taliban is not in control of any of the military section of the airport.
It comes as US forces helping to evacuate Afghans desperate to flee new Taliban rule are on alert for more attacks after a a bomb blast killed 92 people, including 13 US service members, outside the airport yesterday.
Two British nationals and the child of a British national are among those who are confirmed to have been killed so far.
The White House said the next few days of an evacuation operation that has taken more than 100,000 people out of the country in the past two weeks were likely to be the most dangerous.
Some US media said the death toll was far higher yesterday's attack near the airport gates, where thousands of people have gathered to try to get inside the airport and on to evacuation flights since the Taliban took control on 15 August.
The New York Times cited local health officials as saying as many as 170 people, not including the US troops, had died in the attack.
Mr Kirby said the United States believed there are still "specific, credible" threats against Kabul airport.
"We certainly are prepared and would expect future attempts," Mr Kirby told reporters in Washington. "We're monitoring these threats, very, very specifically, virtually in real time.".
US and allied forces are racing to complete evacuations of their citizens and vulnerable Afghans and to withdraw from Afghanistan by a 31 August deadline set by President Joe Biden.
Islamic State (ISIS), an enemy of the Islamist Taliban as well as the West, said one of its suicide bombers had targeted "translators and collaborators with the American army".
The Pentagon said the attack was carried out by one suicide bomber, not two as earlier thought.
The number of Afghans killed has risen to 79, a hospital official told Reuters today, adding that more than 120 were wounded.
A Taliban official said the dead included 28 Taliban members, although a spokesman later denied any of their fighters guarding the airport perimetre had been killed.
General Frank McKenzie, head of US Central Command, said US commanders were watching for more attacks by the so-called Islamic State group, including possibly rockets or car bombs targeting the airport.
"We're doing everything we can to be prepared," General McKenzie said, adding that some intelligence was being shared with the Taliban and he believed "some attacks have been thwarted by them".
The attack underlined the realpolitik facing Western powers in Afghanistan: Engaging with the Taliban who they have long sought to fend off may be their best chance to prevent the country sliding into a breeding ground for Islamist militancy.
It was unclear if ISIS gunmen were involved in the attack or if the firing that followed the blast was Taliban guards firing into the air to control crowds.
Hard-pressed medical staff in the three operating theatres of Kabul's Emergency Hospital worked through the night treating casualties.
"Everybody is concerned at this moment in Kabul, nobody knows what to expect in the coming hours," said Rossella Miccio, president of the Italian aid group that runs the hospital.
US President Joe Biden said yesterday evening he had ordered the Pentagon to plan how to strike ISIS-K, the Islamic State affiliate that claimed responsibility.
The group has killed dozens of people in attacks in Afghanistan in the past 12 months.
"We will not forgive. We will not forget. We will hunt youdown and make you pay," Mr Biden said in televised comments from the White House.
Mr Biden, criticised at home and abroad for the chaos around the final US troop withdrawal even before yesterday's attack, says the United States long ago achieved its original rationale for invading the country in 2001.
The US-led invasion toppled the then-ruling Taliban, punishing them for harbouring al-Qaeda militants who masterminded the September 11 attacks that year.
Taliban guards blocked access to the airport this morning, witnesses said.
"We had a flight but the situation is very tough and the roads are blocked," said one man on an airport approach road.
Another 12,500 people were evacuated from Afghanistan yesterday, raising the total airlifted abroad by the forces of Western countries since 14 August to about 105,000, the White House said.
France has held talks with Taliban representatives in recent days in Kabul and in Doha to ease its ongoing evacuations, the foreign ministry said.
The United States will press on with evacuations despite the threat of further attacks, General McKenzie said, noting that there were still about 1,000 US citizens in Afghanistan.
The pace of flights accelerated today and American passport holders had been allowed to enter the airport compound, according to a Western security official inside the airport.
British Defence Secretary Ben Wallace said the threat of attacks would increase as Western troops got closer to completing the huge airlift and leaving.
"The narrative is always going to be, as we leave, certain groups such as ISIS will want to stake a claim that they have driven out the US or the UK," Mr Wallace told Sky News.
He also vowed action against ISIS wherever it manifests itself.
ISIS-K was initially confined to areas on the border with Pakistan but has established a second front in the north of the country.