United States President Joe Biden vowed to hunt down those behind the suicide bombings that killed 13 American troops in the worst single-day loss for the Pentagon in Afghanistan since 2011.
"We will not forgive. We will not forget. We will hunt you down and make you pay," Biden, visibly shaken, said in an address from the White House during which he said the evacuations of vulnerable people would continue until August 31.
There remained an "opportunity for the next several days, between now and the 31st, to be able to get them out," he 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 Taliban condemned the blasts but pointed out they happened in an area that was under the control of the US military.
The Islamic Emirate strongly condemns the bombing targeting civilians at Kabul airport," a statement released by the group's spokesman on Twitter said.
"The explosion took place in an area where US forces are responsible for security."
British Prime Minister Boris Johnson condemned the attack as "barbaric," paying tribute to the "phenomenal effort" of those involved in the evacuation operation.
He said that Britain would "keep going up until the last moment."
French President Emmanuel Macron expressed "his condolences to the families of the American and Afghan victims" and saluted "the heroism of those who are on the ground to carry out the evacuation operations."
Spanish Prime Minister Pedro Sanchez said: "The international community stands with the Afghan people."
For Poland's President Andrzej Duda, the bombings were an "act of cowardice," while Italian Prime Minister Mario Draghi condemned "this vile and horrible attack against defenceless people seeking liberty."
Norway deplored that "innocent civilians trying to leave the country have become victims of this terrible act of cruelty."
Sweden meanwhile paid tribute to the US service members: "We are grateful for all your efforts in making this historic evacuation operation possible."
China on Friday condemned the deadly attacks, saying Afghanistan still faces a "complex and severe" security situation as the United States withdraws.
The blasts show "the security situation in Afghanistan is still complex and severe," Chinese foreign ministry spokesman Zhao Lijian told reporters on Friday.
"China is shocked by and strongly condemns the explosions," Zhao said, adding that the ministry had not received any reports of Chinese casualties.