The US president and his allies have dismissed the report in The Atlantic as false.
The allegations, sourced anonymously, describe multiple offensive comments by the president about US service members killed or captured in action. Mr Trump allegedly called First World War dead at an American military cemetery in France “losers” and “suckers” in 2018.
The reported comments, many of which were confirmed independently by The Associated Press, shine a fresh light on Mr Trump’s previous public disparagement of American troops and military families.
That opens a new political vulnerability for the US president less than two months from election day.
Voice cracking, Mr Biden told reporters on Friday that “you know in your gut” Mr Trump’s comments, if true, are “deplorable”.
Mr Biden added: “I’ve just never been as disappointed, in my whole career, with a leader that I’ve worked with, president or otherwise.
“If the article is true – and it appears to be, based on other things he’s said – it is absolutely damning. It is a disgrace.”
Every day Donald Trump proves how morally unfit he is to lead our nation.
In 60 days, we have to vote him out. https://t.co/EteeruIOm6— Joe Biden (@JoeBiden) September 5, 2020
He added that “the president should humbly apologise to every Gold Star mother and father, to every Blue Star family that he’s denigrated. … Who the heck does he think he is?”
Mr Trump, in the Oval Office, said no apology was necessary, because it was a “fake story”.
The US leader is alleged to have made the comments in November 2018, as he was set to visit the Aisne-Marne American Cemetery during a trip to France.
The White House said the visit was scrubbed because foggy weather made the helicopter trip from Paris too risky, and a 90-minute drive was deemed infeasible.
The Atlantic story on @realDonaldTrump is total BS. I was actually there and one of the people part of the discussion - this never happened. I have sat in the room when our President called family members after their sons were killed in action and it was heart-wrenching...
— Sarah Huckabee Sanders (@SarahHuckabee) September 4, 2020
Speaking on Friday in the Oval Office, Mr Trump denied ever uttering such comments: “It was a terrible thing that somebody could say the kind of things – and especially to me, ’cause I’ve done more for the military than almost anybody else.”
Later, in a press briefing, Mr Trump suggested the source of the story was his former chief of staff, retired Marine General John Kelly.
“It could have been a guy like John Kelly,” Mr Trump told reporters, saying his former top aide “was unable to handle the pressure of this job”.
Mr Biden’s critique was personal. The former vice president often speaks about his pride for his late son Beau’s service in the Delaware Army National Guard.
As he spoke, Mr Biden grew angry, raising his voice to rebut Mr Trump’s alleged comments that Marines who died in battle were “suckers” for getting killed.
“When my son was an assistant US attorney and he volunteered to go to Kosovo when the war was going on, as a civilian, he wasn’t a sucker,” Mr Biden declared.
“When my son volunteered to join the United States military as the attorney general, he went to Iraq for a year, won the Bronze Star and other commendations, he wasn’t a sucker.”
Beau Biden died of cancer in 2015.
Returning to Washington from a Thursday visit to Pennsylvania, Mr Trump told reporters that the Atlantic report was “a disgraceful situation” by a “terrible magazine”.
“I would be willing to swear on anything that I never said that about our fallen heroes,” Mr Trump told the reporters, gathered on the tarmac in the dark.
“There is nobody that respects them more. No animal – nobody – what animal would say such a thing?”
Mr Trump also denied calling the late Arizona senator John McCain, a decorated Navy officer who was a prisoner of war in Vietnam, a “loser” after his August 2018 death.
The US president acknowledged on Thursday he was “never a fan” of Mr McCain and disagreed with him, but said he still respected him and approved everything to do with his “first-class triple-A funeral” without hesitation because “I felt he deserved it”.
In 2015, shortly after launching his presidential candidacy, Mr Trump publicly blasted McCain, saying, “He’s not a war hero.”
He added: “I like people who weren’t captured.” At the time, Mr Trump also shared a news article on Twitter calling Mr McCain a “loser”.
