WASHINGTON — President Bush would veto any bill drafted by House Democratic leaders that would fund the Iraq war only into summer, his spokesman said yesterday, even as the Pentagon held out hope that troops could begin withdrawing if the Iraqi government makes progress by fall.

Defense Secretary Gates told a Senate committee that if violence in Iraq declines enough to allow the government to move forward, including steps toward political reconciliation, the U.S. could begin pulling troops out.

The Pentagon, Mr. Gates said, is ” looking for the direction of events — we don’t have to have it all locked in place and everything complete … If [we] see some very positive progress and it looks like things are heading in the right direction, then that’s the point at which I think we can begin to consider reducing some of those forces.”

He added that “getting the level of violence in Iraq to point where the political process can go forward and seeing some progress in reconciliation sets the stage for us to begin withdrawing our units … and allowing those security responsibilities to be assumed by the Iraqis.”

Senators pressed Mr. Gates on reports that commanders in Iraq may want to wait until next April to make an assessment of the buildup.

But Mr. Gates insisted that the evaluation would be in September, although he added that he didn’t know what the result would be.