The US president is facing a firestorm of criticism for the chaotic evacuation from Afghanistan.
US President Joe Biden has acknowledged the mass evacuation from Afghanistan is “not without risk of loss”.
Speaking at the White House, Mr Biden said the US had rescued 13,000 people to date in “one of the largest, most difficult airlifts in history”.
But the president’s suggestion that US evacuees were not being hampered by the Taliban was contradicted by his own defence secretary.
Mr Biden has faced international blowback over the Taliban’s takeover.
“Any American who wants to come home, we will get you home,” said Mr Biden, who cut short his holiday to address the crisis.
Taking questions from reporters, the president said the US military would make the “same commitment” to 50-65,000 Afghan allies hoping to leave, before adding the evacuation of American citizens was the “priority”.
“Make no mistake, this evacuation mission is dangerous. It involves risks to our armed forces and it’s being conducted under difficult circumstances,” said Mr Biden.
“I cannot promise what the final outcome will be or that it will be without risk of loss. But as commander in chief, I can assure you that I will mobilise every resource necessary,” he added.
He also said it would not be necessary to send US troops into Kabul to extract trapped Americans, claiming that the Taliban was permitting airport entry to anyone holding a US passport.
However, numerous reports from Kabul have suggested US citizens are having trouble reaching the airport. And Defence Secretary Lloyd Austin told lawmakers in a briefing on Friday that Americans trying to leave Afghanistan have been beaten by Taliban fighters, reports Politico.
The Biden administration has been questioned repeatedly this week on how the US intelligence service seemed to so seriously misjudge the situation in Afghanistan.
On Friday, Mr Biden again rejected the notion of an intelligence failure, saying there was a “consensus” among officials that the Taliban surging to power this quickly was “highly unlikely”.
The president also pushed back on the suggestion that events in Afghanistan had tarnished the US reputation on the world stage, insisting there had been “no question of our credibility from our allies around the world”.
Describing the war in Afghanistan as a “joint effort” with allied countries, Mr Biden said he would convene a meeting with G7 allies to discuss next steps.
On Friday, South Carolina Republican Senator Lindsey Graham said if the US leaves one US citizen or Afghan ally behind, Mr Biden should be impeached.
Several Democrats have also criticised Mr Biden. New Jersey Senator Bob Menendez, who chairs the powerful Senate Foreign Relations Committee, said he plans to seek a “full accounting” of what he described as the “flawed” withdrawal from Afghanistan.
The president said the scenes out of Kabul in recent days were “heartbreaking”. Images from Afghanistan’s capital show hordes of people desperately trying to flee as the Taliban tightens its grip on the country.
Tens of thousands of people are still waiting to be evacuated ahead of the looming 31 August deadline for the US withdrawal. Mr Biden suggested earlier this week he would consider keeping US forces in Afghanistan beyond that date to ensure the evacuation of all US citizens.
The US has nearly 6,000 troops on the ground in Afghanistan to help the evacuation effort and maintain control at the airport in Kabul, Mr Biden said.
But those seeking to leave Afghanistan face massive crowds and Taliban checkpoints just to reach the airport.
The US has maintained constant contact with the Taliban, Mr Biden said.
Asked by reporters on Friday if the US would consider expanding its security perimeter outside the airport, Mr Biden said such a move would probably lead to “unintended consequences”. He did not specify what those might be.
US forces in three Chinook military helicopters left Kabul airport on Friday to help bring 169 American citizens to the runway, according to the Pentagon.
Defence department spokesman John Kirby said troops had ventured beyond the perimeter for a “short” amount of time to a hotel just 200 metres (656ft) away.
It is the first time US troops are known to have moved into the city since Kabul’s fall.
Nato Secretary General Jens Stoltenberg told reporters on Friday: “We have more planes than we have people or passengers because the process of getting people – especially Afghans – into the airport and processed is now the big, big challenge.”
Also Friday, US flights out of Kabul were suspended for several hours due to processing delays in Qatar, the destination country.
State Department spokesman Ned Price later said that 11 countries in the Middle East and Europe had agreed to act as transit countries for Afghan evacuees.
Analysis by Tara McKelvey, BBC White House reporter
Joe Biden struck a note of compassion during his speech, and said he did not think anyone could “see those pictures and not feel pain”.
He was referring to the horrifying images of people trying to flee Afghanistan. His remarks sounded like the old Biden, so long depicted by admirers as an empathetic figure.
It was different from the remarks that he made earlier in the week, when he struck a defiant tone about his decision to withdraw the troops. Voters – both Democrats and Republicans – wonder about his strategy, and resent the way that he blamed others, whether Donald Trump or the Afghan army, for the catastrophe.
His approval rating is now at its lowest point – 49% – since taking office, according to the poll tracker FiveThirtyEight, showing many voters have misgivings about his leadership.
The president is trying to win them back, but for many, his efforts are too little, too late.