"Secretary Rumsfeld's energetic and steady leadership is exactly what is needed at this critical period," George Bush said in a statement on Friday.
"He has my full support and deepest appreciation."
Bush stepped in after six retired generals came forward one after another to press for Rumsfeld's ouster, exposing a deep vein of discontent with his leadership within the military.
The generals, several of whom held key combat commands and staff positions, accused Rumsfeld of an arrogant disregard for military advice and for providing too few troops to pacify Iraq.
But Bush praised Rumsfeld's leadership, noting he was charged with the difficult challenges of fighting wars in Iraq and Afghanistan while undergoing an institutional transformation of the military.
"I have seen first-hand how Don relies upon our military commanders in the field and at the Pentagon to make decisions about how best to complete these missions," Bush said.
Rumsfeld himself rejected the calls for his ouster in an interview with Dubai-based Al Arabiya television that aired on Friday but was conducted on Thursday.
"I intend to serve the president at his pleasure," he said.
He said the retired generals had a right to their views. "But obviously if, out of thousands and thousands of admirals and generals, if every time two or three people disagreed we changed the secretary of defence of the United States, it would be like a merry-go-round," he said.
He also rejected criticism that he had not given his commanders the troops they needed to pacify Iraq, a key contention of the retired generals who have accused him of dismissing professional military advice.
Rumsfeld is accused of showing
disregard for military advice
"Personally I'll go with General [John] Abizaid and General [George] Caseys judgement. I think they are probably the best observers," Rumsfeld said, referring to the two top commanders over US forces in Iraq.
"There are people on the outside who are retired, who look back, and say 'Oh this or that,' and that's fine, they can do that, but that doesn't make them right," he said.
The retired generals have called for Rumsfeld's resignation in an unnerving sequence of opinion pieces and television interviews that bitterly criticised his leadership style and the decisions he took in going to war with Iraq.
With one after another voicing similar complaints, the calls have taken on the appearance of a choreographed campaign.
But retired major general John Batiste, a former commander of the 1st Infantry Division in Iraq, said it was not orchestrated, but a spontaneous outpouring of discontent that had built over a long time.
"I think it's absolutely coincidental," he said on NBC television.
2360 US soldiers have died so far
in Iraq since the 2003 invasion
Anthony Zinni, a retired marine, added to the pressure for Rumsfeld's scalp by telling CNN that Rumsfeld should be held accountable for a series of blunders, starting with "throwing away 10 years worth of planning, plans that had taken into account what we would face in an occupation of Iraq".
His views were supported by other commanders who served under Rumsfeld.
The demands for Rumsfeld's departure came as opinion polls show eroding public support for the three-year-old Iraq war in which about 2,360 US troops have died and Bush is struggling to bolster Americans' confidence in the war effort.