Washington (CNN) US Secretary of Defense James Mattis said Monday he has "never talked" with President Donald Trump about leaving the administration despite the President's calling him "sort of a Democrat" who "may leave" his position.

"I'm on his team. We have never talked about me leaving," Mattis told reporters during a flight to Vietnam to meet with senior Vietnamese officials, according to a Department of Defense transcript. Mattis was responding to Trump's comments during an interview with "60 Minutes" that aired Sunday. "And as you can see right here, we're on our way. We just continue doing our job."

Mattis also dismissed the President's remark suggesting he had affiliation with the Democratic Party. "I've never registered for any political party," he said.

In his wide-ranging interview with "60 Minutes," Trump sparked speculation that Mattis' days may be numbered after saying he was unsure about the defense secretary's future in the administration. "He may leave. I mean, at some point, everybody leaves. Everybody. People leave," the President said. "That's Washington."

Trump added that he and Mattis "get along very well."

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