Asked at a Pentagon briefing whether he would consider resigning to ease political pressure on Mr. Bush and Republicans in Congress, Rumsfeld said, "No.
"The president knows, as I know, there are no indispensable men ... He knows that I serve at his pleasure, and that's that," Rumsfeld said.
Rumsfeld spoke several hours after Mr. Bush reiterated his support for Rumsfeld during a Rose Garden news conference announcing. "And what's best is for Don Rumsfeld to remain as the secretary of defense," the president said.
It wasn't just what Mr. Bush said, reports CBS News chief White House correspondent Jim Axelrod, but how he said it — forcefully and definitively.
"I have strong confidence in Don Rumsfeld. I hear the voices. And I read the front page. And I know the speculation. But I'm the decider and I decide what is best. And what's best is for Don Rumsfeld to remain as the secretary of defense."
Rumsfeld said he is proud of his five-year tenure of overseeing the Pentagon through wars in Afghanistan and Iraq and a major restructuring of the armed forces.
He suggested that many in the military were naturally resistant to changes.
"These are important issues that are involved. There's no question about that. Change is difficult. It also happens to be urgently necessary," Rumsfeld said.
Under his leadership, he said, the first Marine Corps general — Peter Pace — has been promoted to chairman of the Joint Chiefs of Staff.
Many expensive weapons systems have been canceled, like the Crusader mobile artillery system, and some U.S. forces have been brought home from Europe and South Korea.
"I look back on those decisions and I am proud of them. They caused a lot of ruffles," Rumsfeld said.
Within the past month, six retired generals have called for Rumsfeld to resign, accusing him of mishandling the Iraq war, ignoring advice of military commanders and having an arrogant management style.
Rumsfeld says he's being targeted because he's an agent of change — the man in charge of transforming the military into a 21st century fighting force.
But, reports Axelrod, one of the retired generals, two-star Gen. John Batiste, says they are not targeting him because he's an agent of change, but because of his flawed battle plan in Iraq.
"With all due respect, this has nothing to do with change," Batiste told Axelrod. "The military's been changing for a very long time. The issue again is accountability for very poor strategic decisions that have essentially put us where we are today. What should have been a very deliberate victory is now a protracted challenge."
"Many of the complaints that have come out have more been about events after the invasion of Iraq. Abu Ghraib, the decision to disband the Iraqi army, dismissing the insurgency," explained CBS News Military Consultant, Retired Army Col. Jeff McCausland. "And really they seem to call more for a level of accountability that we haven't seen either for senior military officers or for senior government officials. And that's something I've heard frequently from many senior officers."
In what seemed to be a swipe at such critics, Rumsfeld said, "People who are often talking about what's taking place inside here don't know what's taking place inside here."
As to the recent criticism of him from one-time commanders, Rumsfeld said, "We should be reasonably tolerant with respect to things that get said."
Asked whether there was any validity to the criticism of him, Rumsfeld said, "Well, you know, I've been hearing all about all of this, and I would prefer to let a little time walk over it.
"I think that because of the importance of these matters that are being discussed, I'd like to reflect on them a bit," Rumsfeld said.
Meanwhile, Sen. Dick Durbin of Illinois, the second-ranking Senate Democrat, said Tuesday that Democratic senators have discussed trying to force the Senate to take a symbolic vote testing the support Rumsfeld has when Congress returns next week from its spring recess.
Durbin has said Rumsfeld should step down.
"I think we need to have a vote of confidence on Secretary Rumsfeld. Let the Senate go on record," Durbin told reporters in Springfield, Ill.