According to the new report in The Atlantic by Jeffrey Goldberg, Trump referred to American service members killed in war as "losers" and "suckers" and canceled a visit to a cemetery for American soldiers outside Paris in 2018 because he didn't think it was important to honor them.
ABC News has not independently confirmed The Atlantic report, which cites four unnamed sources with direct knowledge in making the claims.
Landing in Washington late Thursday night after a campaign rally in Pennsylvania, the president -- visibly angry -- delivered a seven-minute diatribe to reporters who had traveled on Air Force One.
"I would be willing to swear on anything that I never said that about our fallen heroes. There's nobody that respects them more," Trump said.
The president insisted the story is fabricated and suggested the anonymous sources were former officials who did not succeed in their roles in the administration.
"They made it up and probably it's a couple of people that have been failures in the administration. That I got rid of, and I couldn't get rid of them fast enough. Or it was just made up," he said.
Trump again denied the report in a press conference Friday afternoon, calling it a "hoax" and comparing it to the Russia investigation.
"There is nobody that feels more strongly about our soldiers, our wounded warriors, our soldiers that died in war, than I do," Trump said. "It's a hoax, just like the fake dossier was a hoax, just like the Russia, Russia, Russia was a hoax. It was a total hoax. No collusion. Just like so many other things, it's a hoax. And you'll hear more of these things, totally unrelated, as we get closer and closer to election."
Two aides who were at the president's side on the trip when the comments were alleged to have happened have also come forward to issue forceful on-the-record denials that the president made the disparaging comments alleged in the report.
"I was actually there and one of the people part of the discussion -- this never happened," Sanders wrote.
The president's deputy chief of staff for communications, Dan Scavino, also tweeted, calling the report "complete lies by 'anonymous sources'" and a "disgusting" attempt to smear the president ahead of the election.
Former national security adviser John Bolton, who wrote a book critical of the president and who was with Trump on the trip to France when the cemetery trip was canceled, told ABC News he didn't hear the president refer to dead American service members as "suckers" or "losers."
Bolton said that while he can't rule out that the president made the comments at another time, he was there for discussions on canceling the president's trip to the cemetery and didn't hear anything like what is reported in The Atlantic.
The president's forceful denial comes as he seeks to shore up support among the military ahead of the November election, with polls showing the president trailing Democratic nominee and former Vice President Joe Biden.
"To think I would make statements negative to our military and our fallen heroes when no one has done what I've done-with the budgets, with getting pay raises for our military," Trump said. "All they're trying to do is influence a presidential election."
In remarks Friday, Joe Biden slammed the comments attributed to Trump in The Atlantic article.
"If what is written in The Atlantic is true it is disgusting. It affirms what most of us believe to be true. Donald Trump is not fit to be the job of president to be the commander in chief," Biden said. He later added: "If these statements are true, the president should humbly apologize to every gold star mother and father and every blue star family. Who the heck does he think he is?"
His campaign spokesperson, Andrew Bates, later added in a statement, "Not only is it a quantifiable reality that Donald Trump is the most dishonest president in American history, but he's also one of the least credible human beings alive. How does that stack up next to the word of senior Marine Corps officers, DoD officials, and four other people with direct knowledge of these statements? Not well."
While Trump expressed disbelief at the story's claims, he has a history of making disparaging comments about members of the military who have been prisoners of wars. He most famously attacked the late Sen. John McCain and said the five years McCain spent in a North Vietnam prison do not make him a hero.
"He's not a war hero," Trump said of McCain in 2015. "I like people that weren't captured. OK? I hate to tell you."
Thursday night, Trump tried to recast the narrative of his criticism of McCain by boasting that he approved the plans for McCain's funeral in 2018.
"All of that had to be approved by the president. I approved it without hesitation, without complaint. And I felt he deserved it. I disagreed with him. He was a tough guy," Trump said.
Again at a press conference Friday the president said he respected McCain, but he "never got along" with the late senator: "That doesn't mean I don't respect him. I respected him. But I really disagreed with him on a lot of things. And I think I was right. I think time has proven me right to a large extent."
The president, who has continued to criticize McCain even after his death, was not invited to attend the late senator's funeral.
ABC News' Jonathan Karl, Ben Gittleson and Averi Harper contributed to this report.