WASHINGTON (Reuters) - President George W. Bush won a battle over nearly $100 billion to fund the Iraq war as congressional Democrats on Tuesday abandoned troop withdrawal efforts for now but pledged to try again in July.

Instead of setting schedules for withdrawing U.S. troops, it appeared the Democratic-run Congress and the Republican White House agreed for the first time to include conditions prodding Baghdad to make better progress toward quelling violence or risk losing some U.S. reconstruction aid.

“We’ve been led to believe that that is the language that is likely to be in the final version,” Senate Republican leader Mitch McConnell of Kentucky told reporters.

That provision passed the Senate last week, with a few Democrats supporting it. At the time, Senate Majority Leader Harry Reid of Nevada said of the language crafted by Virginia Republican Sen. John Warner: “If you look in the dictionary under ‘weak’ the Warner amendment would be listed under it.”

White House spokesman Tony Snow said the measure would provide “the funding and flexibility the forces need. That’s what we’ve wanted all along.”

On May 1, Bush vetoed Congress’ first version of this year’s emergency war funds bill because it set an October 1 deadline for starting to pull most of the 147,000 soldiers out of Iraq, a goal of anti-war Democrats.

House Majority Leader Steny Hoyer, a Maryland Democrat, said lawmakers were putting the finishing touches on a new bill, and acknowledged the political realities.

Iraqi women walk near U.S. and Iraqi soldiers patrolling the streets looking for weapons and insurgents in Baghdad May 21, 2007. REUTERS/Eduardo Munoz

“The president has made it very clear he’s not going to sign timelines (for withdrawing troops). We can’t pass timelines over his veto,” he told reporters.

DISAPPOINTMENT FOR SOME DEMOCRATS

That will be a disappointment for some Democrats who say they won control of Congress last November largely because voters wanted to see an end to the 4-year-old war in Iraq. But it was welcome news for Republican leaders who have argued Congress should not be “micro-managing” the war.

“Democrats have finally conceded defeat in their effort to include mandatory surrender dates in a funding bill for the troops,” said House Minority Leader John Boehner of Ohio.

Some Democrats have predicted for months that it would take longer to force troop withdrawals. They argue that even with a weaker bill, they have ended four years of “rubber stamp” war funding bills of the previous Republican-run Congress.

Hoyer and Reid said Democrats would continue pushing for a “change in direction” in Iraq, where at least 3,420 U.S. soldiers have been killed and more than 34,000 wounded.

“Certainly we’ll do it in July when Mr. Murtha’s bill is on the floor,” Hoyer said.

In the meantime, Democrats are fully funding Bush’s war financing request.

Pennsylvania Democratic Rep. John Murtha has led efforts in the House of Representatives to end U.S. combat in the Iraq war. In July, Murtha will shepherd a military funding bill through the House for the next fiscal year, starting October 1.

Bush and most Republicans have argued that setting dates for withdrawing U.S. troops would rob military commanders of the flexibility they need to conduct the war.

Despite those charges, even some congressional Republicans, Boehner among them, have spoken of autumn as the timeframe for reassessing progress in Iraq and possibly producing “Plan B.”

Under the Democrats’ latest strategy, the war funding bill will pay for combat in Iraq and Afghanistan through September. Aides said there would be benchmarks for measuring Iraq’s progress toward stability and setting up a competent army.

There would also be consequences for Iraq not meeting the benchmarks, the aides said -- likely to be limits on about $1.6 billion in reconstruction aid, as in Warner’s proposal.