Mr Biden also said the US is committed to evacuating all Afghans who assisted the war effort - seen as a potential expansion of the airlift so far.
It could be interpreted to include the tens of thousands of Afghan translators and others and their close family members, seeking evacuation.
He called the past week “heartbreaking,” but insisted his administration was working hard to speed up evacuations.
“I don't think anyone of us can see these pictures and not feel that pain on a human level,” he said, but “now I'm focused on getting this job done”.
The comments came as the US struggled to step up the massive airlift clearing Americans and vulnerable Afghans through the Kabul airport.
The president is facing criticism at home and abroad for a chaotic and violent scene outside the airport as crowds struggle to reach safety inside.
Evacuation flights at the Kabul airport had stopped for several hours on Friday because of a backlog at a transit point for the refugees, a US airbase in Qatar, officials said.
However, flights resumed later in the afternoon.
As many as three flights out of Kabul were expected in the next few hours, going to Bahrain and carrying around 1,500 evacuees, an official added.
In Washington, some veterans in Congress were calling on the Biden administration to extend a security perimeter beyond the Kabul airport so more Afghans can make it to the airport for evacuation.
They also want Mr Biden to make clear an August 31 deadline for withdrawing US troops is not a firm one.
Tens of thousands of people remain to be evacuated ahead of the United States' August 31 deadline to withdraw its troops from the country, although the pace had picked up overnight.
A defence official said about 5,700 people, including about 250 Americans, were flown out of Kabul on 16 C-17 transport planes.
On each of the previous two days, about 2,000 people were airlifted.
It comes amid chaotic scenes outside the airport throughout the week, with crowds gathered for days waiting to gain entry to flights.
Some of those in the throng of people could be seen clutching UK or European passport, while desperate mothers passed babies to American troops over barbed wired fences.