WASHINGTON -- The top U.S. commander in Iraq, Gen. David Petraeus, told a Senate panel Thursday that he may make a decision on troop levels in Iraq by September.

"My sense is that I will be able to make a recommendation at that time for some further reductions," the four-star Army general said at his confirmation hearing to become the head of U.S. Central Command.

Sen. Carl Levin, chairman of the Senate Armed Services Committee, responded: "That's good news to most of us."

Petraeus also urged lawmakers to give the military more time to make progress.

"In Iraq, Iraqi and coalition forces continue to build on the security gains of the past 15 months as we also continue to reduce U.S. forces and transition responsibility to Iraqi security forces, strive to maintain the conditions necessary for political progress, help build governmental capacity, and seek to foster economic development," he said.

Last week saw the lowest number of security incidents in the country in more than four years, Petraeus told the committee.

The testimony comes as Sens. John McCain and Barack Obama, having virtually secured their nominations, appeal to centrist voters who will decide the fall presidential election.

And on other action Thursday, Senate Republicans broke with President George W. Bush to help Democrats add help for veterans and the unemployed to a bill paying for another year of the Iraq and Afghanistan wars.

The 75-22 vote also adds billions of dollars in other domestic funds such as heating subsidies for the poor and money for fighting wildfires to the $165 billion for the military operations overseas.

McCain recently suggested 2013 as a possible end to U.S. involvement in Iraq. Many saw it as a switch from his earlier denouncements of timelines, although McCain insisted it was not.

Obama continues to tell audiences he will remove U.S. combat troops within 16 months of taking office. Sometimes he seems to shorten it to 11 months, saying, "I will bring this war to an end in 2009."

But his top aides are careful to note several caveats he has embraced, even if he rarely emphasizes them. They include leaving an unspecified number of "residual forces" in Iraq and promising to listen to military advisers before making final decisions.

"Our best estimate is that we can get the bulk of our combat brigades out within 16 months," Susan Rice, a top military adviser to Obama, said in an interview. "It's a timeline, it's a goal."

Economic worries, coupled with an Iraq that is less violent than it was a year ago, have pushed the five-year-old war from the top of voters' concerns and off many front pages. But it will get plenty of attention this week as Petraeus testifies before Congress and the candidates hit military themes for Memorial Day.

Declaring that U.S. "strategic objectives are within reach" in both Iraq and Afghanistan, Secretary of Defense Robert Gates also cautioned again against impatience in Iraq, speaking Wednesday night at U.S. Central Command conference in Tampa, Fla.

"In congressional testimony a few weeks back, I noted that we are now seeing what the end game in Iraq looks like, with our forces drawing down over time in a series of very complex battlefield rearrangements that slowly cede more responsibility for day-to-day security operations to the Iraqis," Gates said. "It is a slow process -- slower than many would have wished, including myself. But it is necessary if we are to get the end game right."

"I fear that frustration over slow progress and dismay over sacrifices already made may result in decisions that are gratifying in the short term but very costly to us in the long term," Gates said. "We are at war in Afghanistan today because of mistakes we made -- I, among others, made -- in the end game of the anti-Soviet war there in the late 1980s. If we get the end game wrong in Iraq, I predict the consequences will be significantly worse."

Many nonpartisan military experts predict that Obama, if elected president, will move more cautiously to disengage from Iraq because a 12-month or 16-month pullout might trigger sharp spikes in violence and political turmoil there.

"I don't know anybody working on this at a senior level who thinks that is plausible," said Brookings Institution military scholar Michael O'Hanlon, who sees important gains from the Bush administration's 2007 "surge" in U.S. troops sent to Iraq.

Even some of Obama's strongest supporters think he is likely, if elected, to take a more deliberate approach to turning Iraq's security over to Iraqi forces.

Obama is "wise not to get too far down in the weeds" of promising exactly how and when he would withdraw U.S. forces, said Matt Bennett, vice president of Third Way, a policy group with centrist-Democratic leanings. "You don't want to tie your hands," he said.

A slower disengagement process would subject Obama to "extraordinary pressure" from infuriated anti-war groups, Bennett said, noting they have helped him outmaneuver Sen. Hillary Rodham Clinton in the primary season.

"The Code Pink people will go into full overdrive," he said, referring to one such group. "But I think Obama will have a lot of latitude" because he would enter the White House with a powerful mandate as a "transformational president."

Whatever the pace, however, Obama would have to withdraw substantial numbers of U.S. forces from Iraq because the Army is nearing a breaking point, Bennett said. Meanwhile, he said, more troops are badly needed in Afghanistan, which Obama calls a must-win war against al-Qaida and its allies.

On the Republican side, McCain caught some supporters and opponents by surprise last week when he stated for the first time that he believes the Iraq war can be won in less than five years.

"By January 2013, America has welcomed home most of the servicemen and women who have sacrificed terribly," he said in an Ohio speech in which he envisioned happy endings to his first term as president. "The Iraq war has been won."

McCain insisted he was not setting a timetable for troop drawdowns, something he has strongly opposed in the past. But the speech triggered a degree of head-scratching in conservative circles, and rebukes from Democrats.

"He's changed his view on some of these major issues, ... announcing he has now, all of a sudden, discovered that we ought to be out of there by 2013," Sen. Chris Dodd, D-Conn., told Fox News Sunday.

Lawrence J. Korb, a military scholar and Obama backer at the Center for American Progress, said McCain envisions victory in 2013, "but he doesn't tell us how he's going to get there." So far, he said, McCain offers the same slogan that has disillusioned so many Americans about the Iraq war. "They keep saying 'wait six more months, wait six more months,"' he said.

In a CBS News/New York Times poll in late April, six in 10 adults said they want the next president to end the war in the next year or two. Almost that many said the United States erred in starting the war. Three quarters said it was more important that the next president stay flexible about when to withdraw troops than to remain committed to winning the war.

Stephen Biddle of the Council on Foreign Relations, who is not affiliated with any candidate, said either McCain or Obama will have to reduce troop levels in Iraq in 2009 because the Army and Marines are being stretched dangerously thin. McCain wants to win a military victory, he said, but "he's not interested in destroying the institution."

Whoever becomes president will confront a public that "harbors mutually contradictory preferences," Biddle said. "They want the troop count down, and they want Iraq stabilized."

It probably is impossible to do both, he said, although some members of Congress say a U.S. withdrawal would force Iraqis to solve their problems.

"I'm not confident in that logic at all," Biddle said. But a partial withdrawal, he said, could result in "the worst of both worlds: enough Americans there to serve as targets, but not enough to keep the country safe."

When the next president confronts Iraq, said Rice, Obama's adviser, "you've got bad options and worse options."