In other words, the former Marine general likes to do keep his head down and do his job with the least fuss a top member of President Donald Trump's cabinet can muster.

But this week, the Pentagon chief found himself smack in the middle of a media firestorm in Washington.

He was the story.

Veteran political reporter Bob Woodward, in his new book about Trump, describes a White House mired in a perpetual "nervous breakdown", with staff battling to corral the angry impulses of a paranoid leader.

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

Mattis moved quickly to deny the claims, but he nonetheless found himself under a spotlight he wants to avoid.

His spokeswoman Dana White said Mattis first learned of the Woodward claims Tuesday, soon after taking off from California for talks in India.

Early on in the 20-hour flight, and after he'd already taken questions from journalists accompanying him, Mattis produced a statement: "The contemptuous words about the President attributed to me in Woodward's book were never uttered by me or in my presence."

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

The statement seemed enough to satisfy Trump, who tweeted it in full and mentioned it in several other messages.

- Apparent differences -

Though Mattis is reluctant to go on camera in Washington -- he has only appeared in the Pentagon briefing room four times and shuns sit-down interviews -- he often stops by the desks of journalists working in the building.

He studiously avoids discussing politics or his relationship with Trump, and has voiced displeasure when the Pentagon press corps highlights apparent differences between him and the president.

To name a few: Mattis had defended parts of the Iran deal, which Trump pulled out of in May.

The Pentagon chief was against the creation of a separate new branch of the US military called Space Force, but Trump ordered it anyway.

And Mattis was on vacation when Trump tweeted that he was banning transgender personnel from serving in the military, only months after they had been allowed in under president Barack Obama.

According to extracts of Woodward's book published by The Washington Post, Mattis had to explain to Trump that the US must keep forces in South Korea "to prevent World War III".

He then reportedly told colleagues that Trump had the understanding of "a fifth- or sixth-grader."

It is not the first time members of Trump's inner circle are purported to have said disparaging things about their leader.

Former secretary of state Rex Tillerson last year reportedly called Trump a "moron".

A few months later, he was gone.

- 'Kill the lot of them' -

Woodward also claims that Mattis, who turns 68 this weekend, has had to talk his boss down from making impulsive decisions.

Following a chemical attack in Syria in 2017, Trump allegedly told Mattis the US should assassinate President Bashar al-Assad and kill the "fucking lot of them".

Woodward writes that Mattis told the president he would "get right on it" but then came back later with plans for a more limited air strike that Trump ultimately authorised.

Trump on Wednesday denied having wanting to kill Assad.

White said Mattis had been unaware remarks ascribed to him were about to appear in the book.

"Mr Woodward never discussed or verified the alleged quotes included in his book with Secretary Mattis, or anyone within the" Pentagon, she told AFP.

Mattis has not spoken to the journalists travelling with him since the news broke.

His work in Delhi, where he met the Indian defence and foreign ministers and Secretary of State Mike Pompeo on Thursday, appears to be on track, with the two nations making a number of arrangements to deepen strategic ties.

"He's a very focused man, and his focus is the lethality of the US forces," White said.

Mattis's overall tenure at the Pentagon has been steady when compared to the chaos that has engulfed several other members of Trump's inner circle.

Traditional allies have embraced Mattis as they look for US reassurance as Trump attacks long-standing deals and institutions.

But in recent months, Trump has made changes to his team of advisors, including by bringing in hawk John Bolton as his national security advisor, prompting numerous stories that suggest Mattis's strong influence may now be on the wane.

How much the Woodward book plays into Mattis's fate remains to be seen.