"The most important thing is to see how sustainable that is. That will depend on how much progress is made towards national reconciliation," the head of the United Nations mission to Iraq, Ashraf Qazi, told Reuters in an interview before Bush's remarks.
Iraq's leaders are expected to get poor marks in Crocker's report to Congress over a series of political benchmarks Washington believes will help heal the deep sectarian rifts.
Iraq's parliament reconvened on Tuesday after a month-long summer recess. It has not yet passed any of the benchmark laws, including measures that would equitably share oil revenues, ease restrictions on former members of Saddam Hussein's Baath Party holding public office, and set a date for provincial elections.
Lawmakers complain the government has yet to submit the draft laws to them.
Parliament adjourned after about 90 minutes after lawmakers asked for time to read 10 bills that had been presented for their consideration, lawmaker Hussein al-Falluji told Reuters. The 10 bills did not include any of the benchmark laws.
Bush flew into Iraq's western Anbar province on Monday, choosing the former Sunni Arab insurgent stronghold once considered a lost cause to showcase what he said was one of the main success stories of his new military strategy.
He hailed what he saw as significant progress in quelling violence in Anbar, a former hotbed of the insurgency where Sunni tribal chiefs have joined with U.S. forces against al Qaeda militants.
Some military analysts point out, however, that the rebellion by Sunni Arab tribes against al Qaeda began before the troop build-up, so caution against using the pacification of the province as proof that the Bush's new strategy is working.
Odierno said Bush told his military commanders he wanted to reduce troop levels from a position of strength, not failure.
"What he said was he's going to listen to the commanders on the ground for their assessment," Odierno said.
"If their assessment is they feel that we can reduce the size of the force while maintaining (the) security and stability we have, then he will consider that and make a decision from that. And he'd be willing to listen to a reduction if that's what we recommend. I think that's where he's at."
Bush is under mounting pressure from Democrats and some senior Republicans who want U.S. troops to start leaving after more than four years of war in which 3,700 U.S. troops and tens of thousands of Iraqis have been killed.
