Facing reporters during a 53-minute news conference, Bush also stood by Defence Secretary Donald Rumsfeld, insisting that the embattled Pentagon chief and Iraq war planner was "doing a really fine job" and would stay on.
Bush also vowed to keep working with Russian President Vladimir Putin despite sometimes sharp disagreements; said "now is the time" to make progress on ending the Middle East conflict and said multilateral diplomacy was the best way to deal with surviving "axis of evil" members Iran and North Korea.
A day after twin bombings killed 66 people in the Iraqi cities of Najaf and Karbala, Bush admitted that violence was taking its toll there, but vowed to press forward with the elections in January.
"There are very hopeful signs but, no question about it, the bombers are having an effect," he said.
"They're trying to shake the will of the Iraqi people and, frankly, trying to shake the will of the American people."
Bush warned Americans that Iraq's elections "are just the beginning of a process" to build democracy and cautioned: "I certainly don't expect the process to be trouble-free."
"Yet, I am confident of the result. I'm confident that terrorists will fail, the elections will go forward and Iraq will be a democracy that reflects the values and traditions of its people," he said.
Bush acknowledged that efforts to train Iraqis to take charge of the country's security had mixed results and noted there had been some cases where security forces had fled when things got difficult.
"That's unacceptable. Iraq will never secure itself if they have troops that, when the heat gets on, they leave the battlefield," he said, adding that he was confident that training efforts would pay off in the long run.
The president remains confident
training efforts will pay off
On the home front, the president shrugged off a question about news reports that the increasingly embattled Rumsfeld did not sign condolence letters to families of US soldiers killed in Iraq, using a machine instead.
"I know secretary Rumsfeld's heart," said Bush. "Beneath that rough and gruff, no-nonsense demeanour is a good human being who cares deeply about the military and deeply about the grief that war causes.
"I believe he's doing a really fine job," he added, hoping to quiet a growing chorus of US lawmakers criticising Rumsfeld and even calling for him to step down or be removed.
Asked about seemingly increasing tensions between Washington and Moscow on issues such as Russian democracy and elections in Ukraine, Bush said he would work to preserve a good personal relationship with Putin.
"It's important for Russia and the United States to have the kind of relationship where if we disagree with decisions, we can do so in a friendly and positive way," he said. "I'll continue to work with him in a new term."
Bush said he sought to preserve
a good relationship with Putin
On the Middle East, Bush said that "now is the time to move the process forward", pointing to upcoming Palestinian elections as a starting point for the eventual creation of an independent Palestinian state.
"It is the beginning of a process," he said. "I look forward to working with the world, the new secretary of state, to work with the Palestinians to develop the structures necessary for a democracy to emerge."
He also gave tepid support to UK Prime Minister Tony Blair's reported plans for a February conference in London to discuss Middle East peace.
And Bush also agreed with former president Bill Clinton's diagnosis that the peace process was like going to the dentist without anaesthesia, joking: "I've been in the diplomatic dental chair for four years."
It was the president's second news conference since winning a second four-year term in 2 November elections.