Amid pressure to speak about the unfolding events in Kabul, the White House said Biden is coming back from Camp David to address the situation later in the day.
CNN's Clarissa Ward said Taliban soldiers had asked her to stand to the side because she is a woman.
"We don't know what to do, we don't know if we still have jobs," Nillan, a Kabul resident, told AP. "It feels like our life and our future has ended."
Rudy Giuliani was quick to criticize Biden, as well as Vice President Kamala Harris and House Speaker Nancy Pelosi, on Twitter.
Desperate scenes at Kabul airport come just weeks after President Joe Biden ordered U.S. troops to entirely withdraw from the country.
The Afghan men were reportedly hanging to the tires of a C-17 U.S. military aircraft before they fell to their deaths.
Graphic videos show chaotic scenes as hundreds of Afghans pile onto planes in a bid to catch a flight out of the country.
Abdulhaq Azad, the press secretary of the Afghan embassy in India, later said the account had been hacked
As Taliban forces enter Kabul, a slow-moving U.S. effort to evacuate Afghan allies has developed into a humanitarian crisis.
"It is time for Joe Biden to resign in disgrace for what he has allowed to happen to Afghanistan," Trump said in a statement on Sunday.
"This was the most irresponsible act, ever. It's just like taking us and putting us before wolves."
"Jihadists all over the world are celebrating this event," Graham warned on Sunday as the Taliban seized control.
The former congressman said the U.S. "could spend additional billions of dollars and lose even more lives, but it would only forestall this outcome and leave us no safer."
The U.S. evacuated embassy personnel in Kabul by helicopter on Sunday as Taliban fighters advanced on Afghanistan's capital.
"There's going to be no circumstance where you see people being lifted off the roof of a embassy," Biden vowed on July 8.
"It does feel like the fall of Saigon today, I'm not going to lie," said Rep. Dingell, a staunch ally of the White House.
The Taliban's relentless advance across Afghanistan came after the withdrawal of U.S. troops from the country in May.
"The security situation in Kabul is changing quickly including at the airport," the embassy said in a security alert Sunday.
"The Trump/Biden calamity unfolding in Afghanistan began with the Trump administration negotiating with terrorists," Cheney said Saturday.
The move comes just hours after Taliban militants entered the outskirts of Kabul and sought the unconditional surrender of the nation's central government.
"I trust the capacity of the Afghan military, who is better trained, better equipped," the president insisted 38 days ago.
The staffer said the flag was "meaningful to him," according to a 'Stars and Stripes' reporter, as workers were told by the U.S. government on Friday to rid of all sensitive materials or items.
"Anything less will further confirm Joe Biden's impotence to the world," said the Arkansas Republican.
"One more year, or five more years, of U.S. military presence would not have made a difference," Biden stated on Saturday.
The Afghan government maintains control of just Kabul and Jalalabad after the Taliban easily took over Mazar-e-Sharif on Saturday.
Even before the U.S. began withdrawing troops, Taliban began reclaiming lost ground. Now the Islamic militant group controls most of the country.
As the U.S. works to wind down a war that has spanned nearly two decades and remove its troop presence from the country, the Taliban is taking over Afghanistan.
"We empowered them to lead, now we are powerless to protect them," Molly Montgomery at the State Department wrote.
Major cities are falling to advancing Taliban fighters with government resistance proving largely ineffective.
"What this is is a reduction in the size of our civilian footprint," U.S. State Department spokesman Ned Price said.