(Adds quotes, background)

By Steve Holland

WASHINGTON, May 21 (Reuters) - President George W. Bush said on Monday he believes September will be an "important moment" to assess the extent of progress in Iraq under his much-criticized troop buildup plan.

Bush, who has rejected timetables for a U.S. pullout from Iraq proposed by Democrats, is under pressure by lawmakers from his Republican Party to show progress in Iraq by September or risk their desertion.

He expects to get an assessment of the impact of the troop buildup plan from the top U.S. commander in Iraq, Gen. David Petraeus, at the end of the summer.

"I see it as an important moment, because David Petraeus says that's when he'll have a pretty good assessment as to what the effects of the surge has been," Bush told Reuters in an interview when pressed on whether he sees September as a make-or-break period.

A group of Republican lawmakers visited Bush privately at the White House earlier this month to express their concerns to him. Bush called it a good session that included a "very frank discussion" of his views about Iraq and "their hopes that we can succeed."

"Very few people come to the White House and say, gosh, I hope we fail. Most people are saying, well, I hope this works, and I am concerned about the situation there," Bush said.

Congress is trying to approve by next week about $100 billion in new funds for U.S. troops fighting in Iraq and Afghanistan because existing funds are running out.

But lawmakers and Bush are embroiled in a fight over whether any conditions should be attached to that money, such as Democrats' desire to impose timetables for ending the 4-year-old war.

Talks last Friday that appeared to be edging toward an agreement ended in acrimony.

Bush said he had directed White House Chief of Staff Josh Bolten to negotiate with lawmakers on what consequences should be imposed to pressure the Iraqi government to meet measurements of progress.

"There is a way forward, there's a compromise to be had. My hope is that the Democrat leader sees it," Bush said.

Lawmakers need to understand that a failed Iraq would embolden al Qaeda, Bush said, adding that he would underscore the point in a speech on Wednesday that "al Qaeda is public enemy number one in Iraq and is public enemy number one for America."

Bush called Iraqi Prime Minister Nuri al-Maliki on Monday and urged him to proceed with political reconciliation among warring groups there, the White House said.

Maliki has been under fire from U.S. lawmakers for not moving quickly enough to gain approval for an oil revenue-sharing law and other measures aimed at a political reconciliation in Iraq.

Bush gave renewed support to Maliki in the phone call marking his first anniversary as prime minister.

"The president reaffirmed his confidence in the prime minister and noted the courage he has shown during a challenging and difficult year," White House spokesman Tony Fratto said.

Maliki stressed his commitment to reconciliation and gave an update on reconciliation initiatives aimed at drawing Sunni Arabs away from the insurgency and into the political process alongside majority Shi'ites and Kurds.

AlertNet news is provided by