Dick Cheney disagreed with President Bush over the president's decision last year to remove Defense Secretary Donald Rumsfeld from office, the vice president told FOX News in an exclusive interview.

Cheney said despite Rumsfeld's controversial handling of the war in Iraq, the secretary of defense was managing the war successfully.

Speaking openly with Bret Baier in the new documentary, "Dick Cheney: No Retreat," the vice president said he "thought that in terms of the way forward, Don was the right guy to continue to lead the Department of Defense."

Click here to view outtakes from the interview.

Cheney had reason to defend Rumsfeld. He was, after all, the man who gave the vice president his start in Washington, D.C.

"I wouldn't be where I am today if it hadn't been for what Don Rumsfeld was willing to do," Cheney said, pointing to "the opportunity he was willing to give me nearly 40 years ago."

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Cheney met Rumsfeld in 1968, when Cheney, then a congressional fellow from Wyoming, and Rumsfeld, a junior congressman from Illinois, were in Washington. The meeting, Cheney would joke later, was his worst job interview ever.

But the meeting apparently left a favorable impression. A few months later, Rumsfeld gave Cheney a shot in Richard Nixon's administration.

"I offered him a position in the ... Office of Economic Opportunity and he came aboard," Rumsfeld said.

After Nixon's resignation, Cheney and Rumsfeld would go on to become a formidable political force in Gerald Ford's administration, and they forged a friendship along the way. When Ford left office, the Cheneys and Rumsfelds shared a family vacation.

"We did," Rumsfeld confirmed for FOX News. "We got in a, in a line at an airport and packed a, a swimming suit and we went down south. And, and the four of us, hah, went on a vacation. Uh, you know, there's a life outside of Washington."

Three decades later, Cheney and Rumsfeld would resurrect their political partnership, this time in the current Bush administration, when Rumsfeld again assumed the defense secretary post after Cheney agreed to become vice president.

"I was really looking for somebody who had seen enough of Washington to be able to be a good confidant," the president said of choosing his vice president.

Cheney said his role as vice president is to serve Bush.

“I do the best I can to give him the kind of advice that I can," Cheney said. "Sometimes he takes it. Sometimes he doesn't.”

When it came time to replace Rumsfeld after the Republicans lost both the House and Senate, Cheney's was an opinion Bush declined to take.

"Well, the way I put is, is that he wished Secretary Rumsfeld hadn't left, and wished to see him remain as the secretary of defense," Bush said, adding, "He's telling you the truth. And that's, that's the truth.”

"Dick Cheney: No Retreat," a rare glimpse into the life of the vice president hosted by Bret Baier and produced by Brian Gaffney, airs at 9 p.m. ET on Oct. 13 on the FOX News Channel.