Mattis, seen as one of the steadiest but also more independent members of Trump's cabinet, has served as a low-profile counterweight to the president in his often abrasive treatment of US allies.

"I'm on his team. We have never talked about me leaving," he told journalists on a flight to Ho Chi Minh City where he is due meet his Vietnamese counterpart.

"We just continue doing our job," he said, adding that he had not spoken with Trump since the comments emerged.

The president described Mattis as "sort of a Democrat," in an interview with CBS's "60 Minutes".

"But General Mattis is a good guy. We get along very well. He may leave. I mean, at some point, everybody leaves," he added.

Asked by reporters about his political affiliation, Mattis demurred, but insisted he had "never registered for any political party".

"My portfolio is bipartisan by its very basis, and that is the protection of the United States. That's what President Trump has told me to do, and I eagerly carry that out," he said.

Rumours that Mattis's days as defence chief are numbered have circulated since a book by journalist Bob Woodward about the chaotic White House said the general had questioned Trump's judgement, likening his understanding of international affairs to that of a 10- or 11-year-old child.

Mattis has been careful to avoid public conflict with Trump, but has nonetheless performed in ways that contrast sharply with his boss, emphatically defending the US commitment to its NATO allies and calling out Russia.

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