The “overwhelming majority” of people eligible for evacuation from Kabul airport have now left Afghanistan, Boris Johnson said, as he promised the UK government will do “everything we can” to get those remaining out of the country.

Speaking to reporters on Thursday morning, the prime minister said “around 15,000” people have already been evacuated by British troops but conceded that time is running out.

“In the time we have left, which may be – as I’m sure everybody can appreciate – quite short, we’ll do everything we can to get everybody else,” he said.

UK and US officials have warned of the increasing risk of a terror attack on the airport, where thousands await evacuation.

Earlier, Armed Forces Minister James Heappey told Sky News a “very lethal attack” could happen in a matter of hours.

The imminent threat has strained the airlift operation to get as many people out of Afghanistan as possible following its takeover by the Taliban.

It is believed many Afghan interpreters and British citizens still need to be evacuated from the country, but the PM told reporters that the “lion’s share” of those eligible for assistance had now been removed from the country.

He did however note that “there will be people who still need help” and said the UK’s commitment to helping those wishing to flee will not end on 31 August – when the US airlift operation will end.

“What we’re hoping, and this is the key point that the G7 agreed, is that the Taliban understand that if they want to engage with development aid, they want to unlock those billions of funds, they want to have a diplomatic, political relationship with the outside world, then the safe passage for those who want to come out is the key precondition,” the PM said.

The prime minister said the UK government must be “transparent about the risks” surrounding the evacuation operation.

“I can’t go into the details, clearly. But we have to be mindful of the security of our personnel, but also of the Afghan people who are trying to get out,” he said.