(Includes Gates response to Clinton complaints)

By Caren Bohan and Susan Cornwell

WASHINGTON, July 20 (Reuters) - President George W. Bush and his generals appealed on Friday for more time to allow his troop increase to work in Iraq, but a U.S. Senate ally said September was still pivotal for evaluating the strategy.

Bush criticized Congress for preparing to leave for an August break without passing a defense policy bill that, among other things, would provide for a pay raise for military personnel and more equipment for the war.

"I also ask Congress to give our troops time to carry out our new strategy in Iraq," Bush said at an appearance with veterans and military families at the White House.

Bush spoke a day after Lt. Gen. Ray Odierno, the No. 2 U.S. commander in Iraq, said while a widely anticipated report in September will indicate how the troop increase is progressing, a fuller assessment would take until November.

Another general, Marine Corps Maj. Gen. Walter Gaskin, who commands U.S. troops in Iraq's Anbar province, said Iraqi security forces will need at least two more years of mentoring and support.

The report due on Sept. 15 from Gen. David Petraeus, the top U.S. commander in Iraq, is considered central to the debate in Congress over whether to force a troop drawdown in Iraq.

Bush has been trying to buy extra time for the troop increase he ordered in January, even though his own Republican Party has grown restive over the unpopular war.

He and his aides have tried do play down the September assessment as a progress report.

Senate Minority Leader Mitch McConnell, a Republican and close Bush ally, said that report was crucial.

"September is the month that we're looking at," the Kentucky senator said. "There may be various generals or various politicians or others who want to mention some other key time, but I think the key time for the vast majority of my members is September."

BUSH, PENTAGON ANGER LAWMAKERS

Even though several prominent Senate Republicans have distanced themselves from Bush's policy, so far most of the dissenters have not been willing to vote for the withdrawal timeline Democrats want. Democrats say they will keep trying to pass a pullout plan until they get the votes.

Bush's criticism of lawmakers for not yet passing the defense policy bill with the soldiers' pay raise angered Democratic leaders, who pointed out the White House had previously opposed the raise as unnecessary.

"While Democrats have fought for a pay raise for our troops all along, the president was against the pay raise before he was for it," said House Speaker Nancy Pelosi.

Defense Secretary Robert Gates, meanwhile, sought to calm a brawl over Iraq that broke out between the Pentagon and Sen. Hillary Clinton, a presidential hopeful.

Clinton, a New York Democrat, was furious with the Pentagon's refusal to give her any information about possible troop pullout plans. Instead, Undersecretary of Defense Eric Edelman told her "premature and public discussion" of withdrawal "reinforces enemy propaganda."

Calling Edelman's response outrageous, Clinton said on Friday she was introducing a bill to demand the information.

Then Gates said he was looking into the matter and would respond next week.

"I have long been a staunch advocate of congressional oversight, first at the CIA and now at the Defense Department. I have said on several occasions in recent months that I believe that congressional debate on Iraq has been constructive and appropriate," Gates said in a statement.

In the near term, the Democrats' drive to change the course of the war is likely to move to the floor of the House of Representatives, which could take up legislation this month to bar permanent U.S. military bases in Iraq and try to attach withdrawal timelines to defense funding legislation.

(Additional reporting by Kristin Roberts)

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