President Bush rallied troops at the U.S. Central Command headquarters in Florida before a meeting with British Prime Minister Tony Blair.
President Bush told soldiers that U.S. troops advancing on the Iraqi capital are up against some of Saddam Hussein's toughest fighters.
"Our military is making good progress in Iraq, yet this war is far from over," the president said. "As they approach Baghdad, our fighting units are facing the most desperate elements of a doomed regime."
Mr. Bush said Republican Guard units defending the Iraqi capital are now under what he called "direct and intense attack."
The president said he can not predict how long the war will last, but is certain that the Iraqi leader's day of reckoning is drawing near.
"Day by day, Saddam Hussein is losing his grip on Iraq. Day by day, the Iraqi people are closer to freedom," Mr. Bush said.
Before the speech, White House spokesman Ari Fleischer said Mr. Bush would declare the war ahead of schedule, but officials say the president decided to delete that line while reviewing the text on Air Force One.
U.S. and coalition forces are facing tough resistance around cities in southern Iraq and on the road to Baghdad where some critical re-supply convoys have been ambushed.
Since the fighting began last week, the president has been trying to downplay public expectations of a swift victory after some military analysts predicted that many Iraqi troops would surrender.
Mr. Bush told members of the U.S. Central Command here that coalition forces are focused and unwavering. He said they will press on through every hardship and overcome every danger to disarm Iraq and topple Saddam Hussein.
"We have no ambition in Iraq except the liberation of its people. We ask no reward except a durable peace. And we will accept no outcome short of complete and final success," the president said.
Mr. Bush had a military briefing and lunch with the troops and some family members of soldiers serving overseas before returning to Washington to meet with British Prime Minister Tony Blair.
Britain is the biggest partner in the U.S.-led coalition against Iraq. Mr. Bush says the alliance is united by the goal of a free and peaceful Iraq and is committed to helping rebuild the country once the fighting is over.
"We will help the Iraqi people to find the benefits and assume the duties of self-government," the president said. "The form of those institutions will arise from Iraq's own culture and its own choices. Yet this much is certain: the 24 million people of Iraq have lived too long under a violent criminal gang calling itself a government."
Prime Minister Blair is expected to urge the president to give the United Nations a leading role in the administration of a post-war Iraq. The two leaders will take questions from the press Thursday before Prime Minister Blair travels to New York for talks with U.N. Secretary-General Kofi Annan.