The prime minister says the UK’s evacuation operation in Afghanistan will continue despite what he described as the “barbaric” terrorist attack at Kabul airport.
An Afghan official has said at least 60 Afghans were killed and a further 143 others wounded.
Marine Corps General Kenneth McKenzie, commander of US Central Command, said 12 US service members were killed in the attack, while 15 more were injured.
The Ministry of Defence said there had been no UK military or government casualties reported so far.
Speaking after a meeting of the government’s emergency COBRA committee, Mr Johnson would not be drawn on who was suspected to be behind the bombings, but said “there were almost certainly members of the Taliban who were themselves killed in this attack”.
Islamic State has since claimed responsibility.
The PM said the threat of a terror attack is “one of the constraints” that those involved in Operation Pitting, the codename for the evacuation operation, have been working under.
“We’ve been ready for it, we’ve been prepared for it,” he said.
“And I want to stress that we’re going to continue with that operation – and we’re now coming towards the end of it, to the very end of it, in any event.”
The PM added: “But, clearly, what this attack shows is the importance of continuing that work in as fast and as efficient manner as possible in the hours that remain to us, and that’s what we’re going to do.”
Mr Johnson said the conclusion from the COBRA committee meeting was that the evacuation programme should continue “in the way that we’ve been running it, according to the timetable we’ve got”.
He added: “That’s what we’re going to do because the overwhelming majority of those who are eligible have now been extracted from Afghanistan.
“We’re going to work flat out, the military, the Foreign Office teams, the Home Office, the Border Force teams that are there getting people through as fast as they can still.
“We’re going to keep going up until the last moment, but I want to repeat what I’ve been saying over the last few days: we also fully expect that those who want to leave Afghanistan after this phase one, if you like, are allowed to do that by the Taliban.”
The PM said the UK’s immediate priority was to “finish off this process of evacuation”, but then things would move into a “second phase” in which G7 and NATO nations will “engage with the Taliban to try to get a political process going that gives a more inclusive future, an inclusive and representative government for Afghanistan”.
Mr Johnson’s comments were echoed by Foreign Secretary Dominic Raab, who has called US Secretary of State Anthony Blinken to “express our sorrow that US troops lost their lives in Kabul today and that more have been injured”.
“I also want to extend my condolences to the families of all those Afghans killed or injured. It is tragic that as they sought safety they have suffered at the hands of terrorists,” he said.
Mr Raab added that the attack was a “stark reminder of the dangerous situation” in Kabul and stressed the UK and US “remain resolute in our mission to get as many people out as possible”.
“It is testament to the remarkable courage of our personnel that they continue to do so while under fire. We will not let the cowardly acts of terrorists stop us,” he said.
An aviation notice advising airlines to avoid Afghan airspace under 25,000 feet has been issued by Transport Secretary Grant Shapps.
Labour leader Sir Keir Starmer described events in Kabul as devastating, adding: “Our thoughts are with all those killed and wounded, serving personnel supporting the evacuations and all those desperately trying to leave.”
Sir Ed Davey, leader of the Liberal Democrats, said: “Tragic and horrifying scenes in Kabul, my thoughts and prayers are with all those who have been injured and the families of the people who have been killed in these senseless attacks.”