Fielding questions from reporters at a year-end news conference, Mr. Bush saidwas "doing a very fine job."
A growing number of lawmakers, including Republicans, have voiced no confidence in the defense secretary. But Mr. Bush defended his Pentagon chief.
"Beneath that rough and gruff no-nonsense demeanor is a good human being who cares deeply about the military and the grief that war causes," Mr. Bush said, batting away criticism that Rumsfeld had not personally signed condolence letters to the families of troops who have died.
Rumsfeld agreed to Mr. Bush's request this month to stay in the Cabinet during the president's second term and has received steadfast support from the White House since.
The 55-minute session, the 17th solo news conference of his presidency, was part of Mr. Bush's effort to seize the momentum from his re-election victory and push several ambitious domestic and foreign policy priorities in his second term.
Much of the Rumsfeld criticism stems from his management of the war in Iraq. Mr. Bush acknowledged that U.S.-trained Iraqi troops are not ready to take over their country's security, and he cautioned that next month's elections there are only the beginning of a long process toward democracy.
The president urged the American people to remain patient well beyond the Jan. 30 elections to give Iraqis time to craft a constitution and strengthen their security forces.
"The elections in January are the beginning of a process and it is important for the American people to understand that," he said.
Critics have raised questions about whether enough U.S. troops are in Iraq to bring security for the elections. Meanwhile, more than 1,300 American troops have died since the war began in March 2003 and soldiers have complained about long deployments and a lack of vital equipment.
"No question about it. The bombers are having an effect" on Americans' belief in success in Iraq, Mr. Bush said, while adding that his own confidence remains unshaken.
Mr. Bush said "I would call the results mixed" on a U.S. effort to put Iraqi security in the hands of its own people. He said U.S. officials in charge of the effort will "spend a lot of time and effort" on fixing the problem by improving the Iraqi command structure.
"There have been some cases where, when the heat got on, they left the battlefield — that is unacceptable," he said. "... We are under no illusion that this Iraqi force is not ready to fight in toto."
On domestic issues, Mr. Bush said he will submit a federal budget that will cut the deficit in half in five years in part by asking for strict spending discipline. His fiscal 2006 budget is due to Congress in February.
"We will submit a budget that fits the times. It will provide every tool and resource to the military, will protect the homeland, and meet other priorities of the government," he said. "It's going to be a tough budget, no doubt about it."
On Social Security, Mr. Bush said he recognized that there would be "difficult choices" but he wouldn't lay out specifics until Congress has a chance to address the issue.
"The first step in this process is for members of Congress to realize we have a problem," he said.
Without any changes, Social Security would begin paying more in benefits than it takes in by 2018.