WASHINGTON – The top American commander in Iraq predicted yesterday that the size of the American fighting force will shrink this year, although he said he had not made new recommendations to his Pentagon bosses on the size and timing of any cuts.

“I’m confident that we’ll be able to continue to take reductions over the course of this year,” Army General George Casey told a Pentagon news conference with Defense Secretary Rumsfeld at his side.

Mr. Rumsfeld said General Casey had not yet had sufficient time to consult with the new Iraqi government, but that in any case the size of the American force is likely to rise and fall in coming months, depending on political and security conditions.

“It will very likely not be a steady path down,” Mr. Rumsfeld said. “It could very likely be a drawdown with an increase.” Noting that there now are 126,900 American troops in Iraq, he said: “It could very well go back up at some point. It very likely will go down and up and down and up depending on the circumstances and depending on the need.”

General Casey, who said more than once last year that he expected to see “fairly substantial” American troop reductions during spring and summer of 2006, noted that the force has dropped from about 138,000 in March to 126,900 now.

“Whether that’s ‘fairly substantial’ enough, I’ll leave to your judgment,” he said. “As I said, I think there will be continued gradual reductions here as the Iraqis take on a larger and larger role.”

The Republican-controlled Senate yesterday soundly rejected two Democratic attempts to urge withdrawal of American troops from Iraq, including an amendment to begin pulling out by the end of the year. GOP lawmakers accused the Democrats of wanting to abandon Iraq before the mission is complete, while Democrats said it is time for changes in Mr. Bush’s failed Iraq strategy.

In an 86-13 vote, the Senate turned back a proposal from some Democrats to require the administration to withdraw all combat troops from Iraq by July 1, 2007, with redeployments beginning this year. No Republicans voted in favor of the plan. Senators Clinton and Schumer of New York also voted against it.

Minutes later, the Senate rejected by 60-39 the proposal more popular with Democrats, a nonbinding resolution that to urge the administration to begin withdrawing troops, but with no timetable for the war’s end.

That vote was mostly along party lines. Siding with all but one Republican were six Democrats – Senators Dayton of Minnesota, Landrieu of Louisiana, Pryor of Arkansas, and three running for re-election this fall: Senators Lieberman of Connecticut, Bill Nelson of Florida, and Ben Nelson of Nebraska.

Asked about the wisdom of setting a fixed date for the start of an American troop withdrawal, General Casey said he opposed that approach.

“I feel it would limit my flexibility,” he said. “I think it would give the enemy a fixed timetable. And I think it would send a terrible signal to a new government of national unity in Iraq that’s trying to stand up and get its legs underneath it.”