Joe Biden has warned those behind the attacks at Kabul’s airport on Thursday: “We will not forgive, we will not forget, we will hunt you down and make you pay.”
The US President was speaking after it emerged that 13 US service personnel were among the 72 people killed after two blasts and a gunfight outside Kabul’s airport.
Some 143 people, including 15 US personnel, were injured in the attack.
Mr Biden said the Americans who were killed in attacks were “heroes” who were “engaged in a dangerous, selfless mission to save the lives of others”.
The UK’s Ministry of Defence has confirmed there were no fatalities among British military personnel or government workers.
Speaking from the White House on Thursday evening, Mr Biden said he had asked for plans to strike back at Isis-K, the Islamic State affiliate believed to have been responsible for the attacks.
He said the US would “find ways of our choosing without large military operations to get them wherever they are”.
Mr Biden also said the US effort to evacuate Americans and the Afghans who helped them will continue, with more troops being sent in if necessary.
He added: “Whatever they need, if they need additional force, I will grant it.”
Analysis by Mark Stone, Sky News US correspondent
A deeply emotional statement from the American president.
He displayed the empathy he has been known for. He drew on his own experiences – a son who served on combat missions; the loss of his own children.
“We have some sense of the feeling…” he said, adding that the loss is like being “sucked into a black hole with no way out.”
But he also attempted to demonstrate power, strength and steadfastness.
“We will not forgive. We will not forget. We will hunt you down and make you pay.” he said of the ISIS-K terrorists.
“We must complete this mission and we will. We will not be deterred by terrorists. We will continue the evacuation.”
He revealed that he believed he knows where ISIS-K terrorists are located and he says he will give commanders on the ground whatever they need.
The attacks have increased the pressure on Mr Biden, who had justified the withdrawal as a means of preventing American deaths in what he described as Afghanistan’s civil war.
On 20 August, after the Taliban took Kabul, Mr Biden told reporters that remaining in Afghanistan any longer could mean he would need to “send your sons, your daughters – like my son was sent to Iraq – to maybe die. And for what? For what?”
But instead of preventing bloodshed, the chaotic evacuation has now resulted in the first US deaths in action in Afghanistan in 18 months.
On Thursday evening, Mr Biden stood by his decision to withdraw from Afghanistan, saying: “It was time to end this 20-year war.”
The deadline for withdrawal agreed between the Taliban and Donald Trump during his presidency last year had been May, but Mr Biden pushed this back to the end of August.
Some European leaders had called for the date to be moved back further but the Taliban warned earlier in the week that such a move would be seen by them as crossing “a red line” and would “provoke a reaction”.