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In an interview set for broadcast Sunday, President Trump speculated whether Secretary of Defense James Mattis might soon leave the administration, just weeks after a book by journalist Bob Woodward reported that Mattis had privately compared Trump to a "fifth- or sixth-grader."

Asked by "60 Minutes" host Lesley Stahl whether Mattis would depart, Trump responded, "Well, I don't know. He hasn't told me that."

He continued: "I have a very good relationship with him. I had lunch with him two days ago. ... It could be that he is. I think he's sort of a Democrat, if you want to know the truth. But General Mattis is a good guy. We get along very well. He may leave. I mean, at some point, everybody leaves. Everybody. People leave. That's Washington."

The president also called reports that the White House is in chaos "so false" and "fake news." He added, "I have people now on standby that will be phenomenal. They'll come into the administration.

"Yeah, other people will go, sure," Trump told Stahl. "We have a great Cabinet. There are some people I'm not happy with. I have some people that I'm not thrilled with. And I have other people that I'm beyond thrilled with."

"Secretary Mattis is laser-focused on doing his job -- ensuring the US military remains the most lethal force on the planet," Pentagon spokesman Army Col. Robert Manning said Sunday in response.

Trump's comments come shortly after U.N. Ambassador Nikki Haley abruptly announced her resignation. They also highlight what some media reports have indicated is an unusually large number of high-level departures from the Trump administration -- figures recently contextualized in an analysis by the nonprofit Brookings Institution.

"We have a great Cabinet. There are some people I'm not happy with."

— President Trump

Woodward's book "Fear," released in September, claimed that Mattis told associates at a National Security Council meeting this year that Trump had the understanding of, and often acted like, a "fifth- or sixth-grader."

WATCH: WOODWARD OPENS UP TO DANA PERINO IN EXCLUSIVE FOX NEWS INTERVIEW

And after Syrian dictator Bashar Assad launched a chemical attack on Syrians in April 2017, Woodward's book reported that Trump demanded Mattis launch an assassination attempt.

“Let’s f---ing kill him! Let’s go in. Let’s kill the f---ing lot of them,” Trump reportedly said. But Mattis, according to the book, told an aide: “We’re not going to do any of that. We’re going to be much more measured.”

According to Woodward, Mattis also was caught by surprise while on vacation about Trump's proposed ban on transgender troops. Mattis, who reportedly opposed the policy, has since unveiled a policy largely adopting Trump's requests, although several lawsuits have temporarily put a hold on enforcing it.

In a statement, Mattis said that “the contemptuous words about the president attributed to me in Woodward’s book were never uttered by me or in my presence.”

Trump, for his part, has openly wondered whether the Pulitzer Prize-winning Woodward is a "Dem operative." In a Twitter post last month, Trump called his book a "con on the public."

Mattis, who Trump named as Defense Secretary in 2016, previously served as head of United States Central Command under former President Barack Obama, replacing David Petraeus. He enlisted in the U.S. Marine Corps Reserve at the age of 18 and became a second lieutenant after graduating from Central Washington University in 1971.

Known as "Mad Dog" Mattis, the defense secretary has openly disagreed with Trump on several key issues. He favored preserving aspects of the Obama-era Iran nuclear deal, which Trump repeatedly maligned as a "horrible, one-sided" giveaway before unilaterally dumping it and restoring sanctions earlier this year.

Mattis, who also took issue with the Obama administration's approach to Iran, criticized parts of the deal, but said it included "robust" oversight measures and overall helped U.S. interests.

Additionally, Trump and Mattis have sparred over the role of NATO, with Trump regularly criticizing its member nations for not contributing more of their GDP to national defense. Mattis views the alliance as a key to maintaining international order.

Mattis further has characterized global warming as a national security threat, while Trump has said the issue is highly politicized and over-emphasized. Last year, he dropped climate change from his national security strategy.

Still, Mattis has turned Trump around to some of his positions. He famously convinced the president to abandon his stated desire to torture terror detainees, and also persuaded him to send more troops to Afghanistan.

Mattis is showing no outward signs of withdrawing from his normal duties. On Tuesday, he will begin his second trip this year to Vietnam, in a sign of how much the Trump administration is trying to counter China's military assertiveness by cozying up to smaller nations in the region. Mattis will visit Ho Chi Minh City, the most populous city and the economic center. It used to be known as Saigon.

The arrival of Deputy National Security Adviser Mira Ricardel to the White House in May has, however, been seen as a sign that Trump is planning to fire Mattis after November midterm elections. Ricardel and Mattis have previously sparred.

Similarly, the hiring of the hawkish former U.N. ambassador John Bolton to be national security adviser in March signaled Trump's shift further to a hardline stance than Mattis is known for advocating. "I heard you're actually the Devil incarnate and I wanted to meet you," Mattis told Bolton in an exchange captured by microphones when they met at the Pentagon earlier this year.

In September, Mattis downplayed reports that he would soon be exiting the Defense Department.

"Somebody cooks up a headline," he told reporters on the steps on the Pentagon. "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 else on the other coast starts writing the same thing — next thing you know you've got a story.

"It'll die down," he added. "How many times have we been through this now, just since I've been here? It'll die down soon and the people who started the rumor will be allowed to write the next rumor, too."

Fox News' Elizabeth Zwirz and The Associated Press contributed to this report.