In a statement the president praised Mr Rumsfeld and said his services are vital to the administration.
"Secretary Rumsfeld's energetic and steady leadership is exactly what is needed at this critical period," said Mr Bush.
"He has my full support and deepest appreciation."
Mr Bush stepped in after six retired generals called for Mr 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 the defence secretary of an arrogant disregard for military advice and for providing too few troops to pacify Iraq.
Mr Rumsfeld himself also dismissed the calls for him to leave.
"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 told Arabic TV channel al-Arabiya.
But he said he did regret the abuse of Iraqi prisoners at Abu Ghraib prison by American troops, and said he offered his resignation in 2004 over the episode, but Mr Bush rejected it.
Bush statement
Mr Bush, who was at the presidential retreat at Camp David, Maryland, praised Mr Rumsfeld's leadership after talking with him earlier on Friday about US military operations.
It is extremely rare for the president to break his holiday and make a statement of this kind.
"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," Mr Bush said.
He pointed out that under Mr Rumsfeld's guidance the US military had undergone a period of brisk change, and faced many major overseas conflicts.
"That kind of change is hard, but our nation must have a military that is fully prepared to confront the dangerous threats of the 21st century," said Mr Bush.
Retired General Richard Myers, the former chairman of the Joint Chiefs of Staff, has also rushed to Mr Rumsfeld's defence.
"My whole perception of this is it's bad for the military, and for military relations, and it's very bad for the country, potentially, because what we are hearing and what we are seeing is not the role the military play in our society," Mr Myers said in an interview with CNN.
The retired generals have called for Mr Rumsfeld's resignation in a recent series of opinion pieces and television interviews that bitterly criticised his leadership style and the decisions he took in going to war with Iraq.
The two most senior generals to voice their concerns were Maj Gen John Riggs and Maj Gen Charles H Swannack Jr, both of them Army.
Gen Riggs said Mr Rumsfeld fostered an atmosphere of "arrogance" among the Pentagon's top civilian leadership.
The retired generals also expressed anger about Mr Rumsfeld's rough treatment of top military officers.
The case most often cited was that of former army chief of staff, General Eric Shinseki, who was rebuked and sidelined after he warned Congress before the war that occupying Iraq would require several hundred thousand troops.
Rumsfeld "allowed abuse"
Meanwhile a report has emerged that Mr Rumsfeld allowed an "abusive and degrading" interrogation of an al-Qaeda Guantanamo Bay detainee in 2002
A report appearing on online magazine Salon, citing an army document, said Saudi national Mohammed al-Kahtani was treated poorly by US soldiers following an interrogation plan approved by the defence secretary.
The report, titled What Rumsfeld Knew, quoted a December 2005 army inspector-general's report in which officers told of Mr Rumsfeld's direct contact with the general overseeing the interrogation at the US naval base at Guantanamo Bay, Cuba.
Over 54 days in late 2002, soldiers forced Kahtani to stand naked in front of a female interrogator, accused him of being a homosexual, and forced him to wear women's underwear and to perform "dog tricks" on a leash, Salon reported.