At the ceremony, Mr Biden was met with hostility from some of the family members of the dead US Marines.
Mark Schmitz, the father of Lance Corporal Jared Schmitz, claimed he showed a picture of his son to the President.
He then said to Mr Biden: “Don’t you ever forget that name. Don’t you ever forget that face.
“Don’t you ever forget the names of the other 12. And take some time to learn their stories.”
Speaking to The Washington Post, Mr Schmitz claimed the President fired back “I do know their stories”.
He then claimed the sister of a dead soldier yelled at Mr Biden after receiving her brothers remains.
She is believed to have said: “I hope you burn in hell! That was my brother!”
Mr Schmitz then told the US outlet: “I can’t fault her for it. We all lost somebody.”
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Marine Lance Corporal Rylee McCollum’s family, one of the 13 Marines who died, was also at Dover Air Force Base on Sunday as his remains returned to the US.
Despite the family being offered the chance to speak with Mr Biden, only his widow, Jiannah McCollum, accepted the meeting.
One of McCollum’s sisters, Roice, told The Post: “He cannot possibly understand. My dad and I did not want to speak to him.
“You cannot kneel on our flag and pretend you care about our troops.
“You can’t f*** up as bad as he did and say you’re sorry. This did not need to happen, and every life is on his hands.
“The thousands of Afghans who will suffer and be tortured is a direct result of his incompetence.”
DON’T MISS
The US Marine’s died on August 26, when ISIS-K sent two suicide bombers to Hamid Karzai International Airport in Kabul, Afghanistan.
The first explosion happened at about 6pm local time (1.30pm BST), close to the Baron Hotel, near the airport’s perimeter.
The hotel was used by British officials to process Afghans hoping to travel to the UK.
It was followed by gunfire and then a second explosion close to the Abbey Gate, one of the airport’s main entrances.
At the White House on Tuesday, Mr Biden vowed there is “no deadline” to help 100 to 200 stranded Americans and thousands of Afghan nationals who worked with the US get out of Afghanistan.
He also defended his decision to pull US forces out of Afghanistan and said: “The war in Afghanistan is now over.
“I’m the fourth president who has faced the decision of whether and when to end this war.
“When I was running for president, I made a commitment that I would end this war. Today, I’ve honoured that commitment.”