US President Joe Biden says he has ordered his commanders to strike the leadership and facilities of ISIS-K after today's attacks in Afghanistan in which dozens of people were killed.

"We will not forgive, we will not forget, we will hunt you down and make you pay," he said, directly addressing those who carried out the suicide bombings near Kabul airport, as well as "anyone who wishes America harm".

Speaking at the White House, President Biden also praised the 12 US troops who died in the attacks, describing them as "heroes".

In the televised address, he vowed that the United States would not be deterred from its mission to evacuate thousands of civilians from Afghanistan despite the deadly blast.

"We will not be deterred by terrorists. We will not let them stop our mission. We will continue the evacuation," President Biden said.

He reaffirmed next Tuesday, 31 August, as the deadline for US troops to leave Afghanistan.

There remains an "opportunity for the next several days, between now and the 31st, to be able to get them out," Mr Biden said.

"Knowing the threat, knowing that we may very well have another attack, the military has concluded that that's what we should do. I think they are right."

The president also said he had seen no evidence that the Taliban colluded with Islamic State militants in carrying out the attacks.

"There is no evidence thus far that I've been given as a consequence by any of the commanders in the field that there has been collusion between the Taliban and ISIS in carrying out what happened today," he said.

Other world leaders also condemned the attacks.

United Nations Secretary General António Guterres said: "I'm following with grave concern the situation at Kabul's airport and strongly condemn today's horrific terrorist attack.

"The incident underscores the volatility of Afghanistan, but also strengthens our resolve as we continue to deliver urgent assistance to the Afghan people."

President of the European Commission Ursula von der Leyen said: "I strongly condemn the cowardly and inhuman attacks on Kabul airport. It is essential to do everything to ensure the safety of people at the airport.

"The international community must work closely together to avoid a resurgence of terrorism in Afghanistan and beyond."

NATO Secretary General Jens Stoltenberg said allied forces should continue to evacuate as many vulnerable people as they can from Kabul despite what he called a "horrific terrorist attack".

"Our priority remains to evacuate as many people to safety as quickly as possible," he tweeted.

Ireland's ambassador to the UN Geraldine Byrne Nason said the deadly explosions near Kabul airport were a reminder of the current "volatility and risks in Afghanistan".

She added that she thought it was likely that the Security Council would discuss the issue soon.

Ireland's mission to the UN, in a post on Twitter, said the attacks were a "tragic realisation of what many of us had feared".

"Our condolences go to the victims of this senseless attack and our solidarity to the women and men of Afghanistan who have endured so much already."

French President Emmanuel Macron condemned "with the utmost firmness the terrorist attacks" near Kabul airport.

In a statement, he expressed "his condolences to the families of the American and Afghan victims, his support for the wounded, and salute to the heroism of those who are on the ground to carry out the evacuation operations", before promising that "France will see them through to the end".

British Prime Minister Boris Johnson said: "I can confirm that there's been a barbaric terrorist attack, what looks like a series of attacks, in Kabul, on the airport, on the crowds at the airport, in which members of the US military, very sadly have lost their lives and many Afghan casualties as well."

He told reporters in Downing Street that the UK evacuation programme would work "flat out" according to "the timetable we've got".

Mr Johnson added: "There were always going to be vulnerabilities to terrorism and opportunistic terrorist attacks.

"We condemn them, I think they are despicable, but I am afraid they are something we had to prepare for."