Gen. David Petraeus testifies Thursday on Capitol Hill in Washington at a Senate Armed Services Committee hearing to confirm him for the Central Command post..

Washington ? Gen. David Petraeus said Thursday he is likely to recommend further troop reductions in Iraq but won’t promise more details until fall – timing that plunges the four-star Army general into the heart of this year’s presidential elections.

The fall assessment would come at a critical time in both American and Iraqi politics. U.S. voters likely will be deciding between a GOP candidate committed to keeping troops in Iraq as long as Petraeus and other ground commanders say is necessary, and a Democratic challenger who supports the immediate withdrawal of forces.

At the same time, Iraq will be headed into its much-anticipated provincial elections, which U.S. officials have described as a crucial step in building national reconciliation by increasing participation by the Sunni minority.

Petraeus said conditions on the ground will still dictate his decision. But by September, when he is slated to assume control of U.S. Central Command, “my sense is that I will be able to make a recommendation at that time for some further reductions,” he said.

Petraeus cautioned that he was not implying that that means a particular brigade or major combat formation. “But I do believe there will be certain assets that, as we are already looking at the picture right now, we’ll be able to recommend can be either redeployed or not deployed to the theater in the fall,” he said.

In a speech at Fort Bragg, N.C., President Bush said progress in Iraq was undeniable and that “we are on our way to victory.” He also said he looked forward to hearing what his generals would recommend, and he didn’t tip his hand as to what he wants to hear.

“My message to our commanders is you will have all the troops, you will have all the resources you need to win in Iraq,” Bush said at the Army base, where he was speaking to 17,000 paratroopers from the 82nd Airborne Division.

In recent months, Petraeus has helped to tame growing opposition to the war in Congress by providing measured assessments of progress and warning that an exodus of U.S. troops would result in chaos.

His unflappable style was on display again Thursday in a Senate Armed Services Committee hearing to confirm him for the Central Command post. The hearing was considerably less contentious than his past appearances on Capitol Hill and even came with an endorsement by the panel’s chairman, Sen. Carl Levin, and Democratic presidential hopeful Hillary Rodham Clinton.

Also receiving a warm reception was Lt. Gen. Raymond Odierno, expected to replace Petraeus as the top commander in Iraq. Odierno previously served 15 months in Iraq as Petraeus’ deputy.

Clinton, D-N.Y., thanked the generals for their “incredible leadership.”

Petraeus has previously been reluctant to say when his next assessment of troop levels might be. This spring he recommended – and Bush agreed – to withdraw by July the 30,000 extra troops sent to Iraq last year as part of a major security push to blunt increasing sectarian violence.

In testimony last month, Petraeus said he needed a 45-day period of evaluation and then an indefinite period of assessment before he would recommend any further pullouts, holding his ground against Democrats demanding to know whether more withdrawals were possible before Bush leaves office in January.