Defense Secretary James Mattis said Monday that he and President Trump have "never" discussed the possibility of Mattis leaving the administration a day after the president stirred speculation of a rift between the pair.

"I'm on his team," Mattis told reporters while en route to Vietnam. "We have never talked about me leaving ... We just continue doing our job."

Mattis has repeatedly dismissed rumors of tensions between himself and Trump. When asked in a "60 Minutes" interview broadcast Sunday if Mattis would leave the administration, Trump said that his defense chief "hasn't told me that" before adding "it could be that he is."

"I think he's sort of a Democrat, if you want to know the truth," Trump told interviewer Lesley Stahl. "But Gen. Mattis is a good guy. We get along very well. He may leave. I mean, at some point, everybody leaves."

When questioned about his political affiliation Monday, Mattis denied he was a registered member of any political party.

"Since I was in the military longer than some of you have been alive, I have seen Republicans and Democrats come and go," Mattis told reporters. "... 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 ... So that's where I stand. That defines me."

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Mattis is scheduled to visit Ho Chi Minh City as part of his second trip to Vietnam in this calendar year. He previously visited Hanoi in January.

Although Vietnam has become a common destination for American secretaries of defense, two visits in one year is unusual, and Ho Chi Minh City is rarely on the itinerary. The last Pentagon chief to visit Ho Chi Minh City was William Cohen in the year 2000; he was the first U.S. defense secretary to visit Vietnam since the war. Formal diplomatic relations were restored in 1995 and the U.S. lifted its war-era arms embargo in 2016.

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The Mattis trip originally was to include a visit to Beijing, but that stop was canceled amid rising tensions over trade and defense issues. China recently rejected a request for a Hong Kong port visit by an American warship, and last summer Mattis disinvited China from a major maritime exercise in the Pacific. China in September scrapped a Pentagon visit by its navy chief and demanded that Washington cancel an arms sale to Taiwan.

Fox News' Lucas Tomlinson and The Associated Press contributed to this report.