Donald Trump has denied allegations that he referred to American soldiers who lost their lives in war as "losers" and "suckers".
The claims date back to 2018 when the US president 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 conservation, 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".
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."
Mr Trump's Democratic rival Joe Biden was quick to jump on the allegations, saying: "If the revelations in today's Atlantic article are true, then they are yet another marker of how deeply President Trump and I disagree about the role of the president of the United States.
"Duty, honour, country - those are the values that drive our service members.
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.
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!"
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."