"My attitude is if he didn't want to continue the drawdown, that's fine with me," Mr. Bush said.
Meeting with General David Petraeus at a U.S. military base in Kuwait, President Bush said the withdrawal of "surge" troops from Iraq is on track.
But as CBS News White House correspondent Bill Plante reports, he cautioned that all decisions about returning troop levels to where they were before the surge will be made by his top commander based on conditions on the ground.
"I made it clear to the general that I need to know his considered judgment about what it takes to keep the security gains we have achieved in place," he said.
"The only thing I can tell you is we're on track for what we've said was going to happen," Mr. Bush said, referring to plans to withdraw some 30,000 "surge" troops from Iraq by July.
However, later Mr. Bush said he is open to the possibility of slowing or stopping altogether any plans to bring home more U.S. troops from Iraq, defying demands among a majority of Americans to speed the withdrawals.
Mr. Bush said the U.S. presence in Iraq will outlast his presidency.
General Petraeus and the American Ambassador to Iraq, Ryan Crocker, are due to give Congress another progress report in March.
The president also defended the Iraqi government, which has made little progress in passing legislation to unify the country - a stated goal for the troop surge and a key indicator of its success.
"I am not making excuses for a government," Mr. Bush said. "To go from a tyranny to a democracy overnight is, uh, virtually impossible."
At the sprawling, dusty brown Camp Arifjan - the largest U.S. base in Kuwait and home to 9,000 American troops - Mr. Bush said, "There is no doubt in my mind that we will succeed. There is no doubt in my mind that when history is written the final page will read, 'History's final victory was achieved by the United States of America for the good of the world.'"
Mr. Bush said the build-up of U.S. troops in Iraq that he ordered one year ago has turned the country into a place where "hope is returning." And he predicted a U.S. force presence in Iraq that would long outlast his presidency.
"We must do all we can to ensure that 2008 will bring even greater progress," Mr. Bush said. He said long-term success in Iraq is vital to stability in the Mideast, and warned that the United States should not turn its back on its friends.
For the troops here and in Iraq, the question is: how many can come home in 2008? The question for Kuwait and the other Arab states the president will visit is: will you support the Israeli-Palestinian peace effort - and help in contain Iran's nuclear ambitions.
After Petraeus and Crocker reported in September, Mr. Bush announced he would withdraw some troops from Iraq by July - essentially the 30,000 sent as part of a buildup ordered a year ago - but still keep the U.S. level there at about 130,000.
Mr. Bush said he and his top general didn't talk about specific troop levels. Instead, the president said they discussed the parameters for continuing to assess the situation leading into the March report, including Mr. Bush's edict that "any position he recommends needs to be based upon success."
"That's what happened the last time," he said.
"It's that same principle that's going to guide my decision. I made that clear to the general," Mr. Bush said.
He defended his decision last year to order a buildup of troops to Iraq, the one that is now scheduled to essentially phase out by this summer.
"The new way forward I announced a year ago changed our approach in fundamental ways," he said. "Iraq is now a different place from one year ago."
Mr. Bush also defended the progress made by the central government in Baghdad, which has lagged in passing legislative reforms seen as key to tamping down the sectarian violence that still plagues the country and hampers other progress.
"What they've gone through to where they are now is good progress," Mr. Bush said, adding it still isn't enough. "They have got more work to do."
One benchmark sought by the United States as a key step toward national reconciliation was achieved today, when.
The voting was carried out by a show of hands on each of the law's 30 clauses. The bill, officially called the "Accountability and Justice" law, seeks to relax restrictions on the right of members of Saddam Hussein's now-dissolved Baath party to fill government posts. It is also designed to reinstate thousands of Baathists in government jobs from which they had been dismissed because of their ties to the party - actions which deepened sectarian tensions between Iraq's majority Shiites and the once-dominant Sunni Arabs.
Later today, during a meeting with Bahrain's King Hamad bin Isa al-Khalifa in Manama, Mr. Bush commended Iraq's parliament for passing the legislation.
"It's an important step toward reconciliation," Mr. Bush said. "It's an important sign that the leaders of that country understand that they must work together to meet the aspirations of the Iraqi people.
"I know you've been concerned about Iraq and the politics of Iraq," Mr. Bush told the king. The president said he was pleased to inform the monarch about the passage of the law.
"I come with an upbeat message, a hopeful message - a message that will prevail here in the Middle East," said Mr. Bush, the first sitting U.S. president to visit Bahrain, an oil-rich nation in the Persian Gulf. Mr. Bush also invited the king to visit him in Washington.
Protesters chanted slogans and waved placards calling on the U.S. to withdraw its military forces from Bahrain. A U.S. base here is home to the 5th Fleet.
Ibrahim Al-Sharif, leader of the opposition Labor Democratic Movement, told demonstrators that President Bush was not welcome in Bahrain.
"He will be mostly welcome if he had come with peace in his hand," Ibrahim said. "We have seen wars in the past and we expect another war."
Saturday's demonstration was the third this week.
On Friday, protesters burned U.S. and Israeli flags after spreading the latter on the ground and stepping on it.
A second protest consisting of some 80 people took place in front of the U.N. headquarters in Manama and was organized by several liberal and Islamic youth organizations and human rights activists.