Joe Biden has said Donald Trump should “humbly apologise” for reportedly calling US war dead “losers” and suckers”.
The Democratic presidential candidate described the president’s alleged remarks as “disgusting” and damnable”.
The claims date to 2018 when Mr Trump cancelled his trip to a cemetery in France,which was blamed on bad weather at the time.
According to The Atlantic, Mr Trump is reported to have asked his aides: “Why should I go to that cemetery? It’s filled with losers.”
In a separate conversation, it is alleged that the president branded US marines who lost their lives at the Battle of Belleau Wood in the First World War as “suckers”.
Mr Trump has denied making the comments.
During a campaign speech in Delaware, Mr Biden said that, if the report is true, “it’s disgusting, and it affirms what most of us believe to be true – that Donald Trump is not fit to be the job of president and be the commander-in-chief.”
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Biden said if The Atlantic article is accurate, “it is absolutely damnable. It is a disgrace.”
He referred to his son Beau, who worked in the US military and later died from cancer in 2015.
“He wasn’t a sucker. The servicemen and women he served with, particularly those who did not come home, were not losers,” Mr Biden said.
He continued: “If these statements are true, the president should humbly apologise to every Gold Star mother and father and every Blue Star family that he’s denigrated and insulted.
“Who the heck does he think he is?”
The Atlantic said it had spoken to four people with first-hand knowledge of the discussion about the cemetery visit, while the Associated Press news agency said a senior defence department official had confirmed some of the remarks, including the 2018 cemetery comments.
However Mr Trump has insisted the claims are “totally false”.
Speaking on Air Force One on Thursday night, the president – who has consistently positioned himself as a supporter of the military and veterans – denied making the comments, calling the site that published the remarks a “terrible magazine”.
“What animal would say such a thing?,” he added.
White House chief of staff Mark Meadows told reporters on the flight: “It’s sad the depths that people will go to during a lead-up to a presidential campaign to try to smear somebody.”
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Mr Biden added that if he is elected president he “will ensure that our American heroes know that I will have their back and honour their sacrifice – always”.
According to The Atlantic, Mr Trump also called Senator John McCain a “loser” upon his death and allegedly refused to support his funeral – claims which the president also denied.
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Mr McCain, who was one of the few major Republican figures who refused to back Mr Trump when he was elected, was captured by opposition forces in the Vietnam War.
Responding on Twitter, Mr Trump said he supported Mr McCain’s funeral and even sent Air Force One to transport his body.
He added: “Also, I never called John a loser and swear on whatever, or whoever, I was asked to swear on, that I never called our great fallen soldiers anything other than HEROES.
“This is more made up Fake News given by disgusting & jealous failures in a disgraceful attempt to influence the 2020 election!”
Via @fitsnews: “Donald Trump: John McCain Is ‘A Loser’” http://t.co/sgiETvdUqi
— Donald J. Trump (@realDonaldTrump) July 18, 2015
In 2015, Mr Trump criticised Mr McCain, saying he “lost” and that “he never liked him as much after that, because I don’t like losers.”
He added at the time: “He’s not a war hero… I like people that weren’t captured.”