The buttoned-up former Marine general is loathe to discuss politics or his dynamic with his mercurial boss, but a new book by veteran political reporter Bob Woodward has thrust the two mens' relationship into the spotlight.

Among other claims, Woodward said Mattis questioned Trump's judgment and likened the president's understanding to that of a 10- or 11-year-old child.

Citing current and former US officials, The New York Times published a story Saturday casting Mattis's future as being in doubt as Trump seeks to surround himself with hardcore loyalists and yes-men.

"It'll die down soon and the people who started the rumor will be allowed to write the next rumor too, just the way this town is," Mattis told Pentagon reporters.

"Keep a sense of humor about it."

Mattis has denied talking to Woodward and said he never likened Trump to a child.

"I wouldn't take it seriously at all," Mattis said.

"It's like most of those kinds of things in this town. Somebody cooks up a headline, they then call to a normally chatty class of people, they find a couple of other things to put in, they add the rumor, somebody on the other coast starts writing the same thing -- next thing you know you've got a story."

Mattis added he has no intention of quitting.

"Of course I don't think about leaving, I love it here," he said.

"I'm thinking about retiring right here, getting a little place down on the Potomac (River)."

Woodward's book describes a chaotic Trump with little understanding of how the government works and an apparent inability to absorb information from his national security team, including Mattis.

While he has acknowledged that policymaking was "inherently messy," Mattis has dismissed Woodward's account as fiction and said his "anonymous sources do not lend credibility."

The many ways the scholarly Mattis's worldview contrasts with that of his boss is an evergreen subject of stories in Washington, a fact that rankles the Pentagon chief, who says he despises being portrayed as an "adult" compared to Trump.