"If they're real, it's beneath the dignity of any commander-in-chief. Truly, they're despicable," Hagel said of the purported remarks in an interview on ABC's "This Week" Sunday.
On Thursday, The Atlantic published the story which described the alleged disparagements and what it described as Trump's private views on the military, resulting in swift and vocal backlash from the president's critics. Trump and numerous members of his staff present for some of the events referenced in the article have denied the report and labeled it a "hoax."
ABC News has not independently confirmed The Atlantic report, which cites four unnamed sources with direct knowledge in making the claims.
Those who have come to the president's defense have been quick to note that the report relies on anonymous sources. Hagel acknowledged that fact Sunday and urged those sources to come forward.
"I think it's important now, if these guys who said this -- or allegedly said it -- think it's that important for the future of this country, then they should show some courage and stuff for it as well," he told "This Week" Co-anchor Martha Raddatz.
But Hagel went on to point out Trump's record of public disrespect toward the late Sen. John McCain and members of his administration who served in the armed services.
"Let's go back and look at Mr. Trump's words himself, coming out of his own mouth, starting in 2016 and what he said about John McCain and what he continued to say about McCain. How he degraded the service of Gens. (James) Mattis and (H.R.) McMaster, and just recently, Gen. (John) Kelly," Hagel said. "The history of -- of this president over the last three and four years is -- is pretty clear."
The president repeatedly clashed with McCain, the 2008 Republican presidential nominee, before the senator's death in 2018. During the 2016 presidential primaries, Trump insulted the more than-five years McCain spent as a prisoner of war during the Vietnam War, saying he likes "people who weren't captured." The president tweeted Thursday that he "never called (McCain) a loser," as claimed in The Atlantic story, but video shows Trump doing just that at a 2015 campaign event.
"He's on the record with saying things himself over the past few years, and that makes the credibility of this article, and those anonymous comments, more and more credible," Hagel said Sunday.
“I disagreed with John McCain on a lot of things,” Trump acknowledged in an exchange with ABC News Chief White House Correspondent Jonathan Karl Friday. “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.”
Hagel, a Republican who served as defense secretary in the Obama administration and represented Nebraska for two terms in the Senate, endorsed Democratic presidential nominee Joe Biden in March, after backing neither Trump or Democratic nominee Hillary Clinton in 2016.
Asked by Raddatz about how the report might resonate in the final two months of the campaign, Hagel predicted that it could have an impact.
"I think it's a pretty clear indictment of this president's attitude toward our veterans," he said, going on to criticize Trump's recent deployment of the military at racial justice protests. "No president has ever done that -- use your veterans, use your active military as props."
Raddatz also spoke with military veterans in the Denver area who shared their reactions to the story, ranging from skepticism about the unnamed sources and a defense of the president's actions on veterans' issues, to blunt condemnations and concerns about active duty troops under his command.
"My immediate reaction was, what is this? This doesn't make a lot of sense. And each allegation was supported by anonymous sources," said one veteran, Nic Gray, who said he "absolutely" did not believe the article.
"I'm a veteran. I served two tours. I have a purple heart. It resonates with me," said Drew Sloane, who served tours in both Afghanistan and Iraq.
"This is someone who has a very me-centric view of the world, and it's hard to have a me-centric view of the world and really understand military service," he said of the president.
"I think this is someone who respects the military vote," Sloane continued. "But that's not the same thing as respecting military service."