BAGHDAD (AP) Face to face with Iraq's leaders, Barack Obama gained fresh support Monday for the idea of pulling all U.S. combat forces from the war zone by 2010.

The Democratic presidential contender also got a military briefing -- and a helicopter tour -- from the top U.S. commander in the region, Gen. David Petraeus, and also met with a few of the nearly 150,000 U.S. troops now well into the war's sixth year.

Back in the U.S., Republican rival John McCain said he hoped the visit would open Obama's eyes to the danger of withdrawal timetables. Said the Arizona senator, who was meeting with President Bush's father, the former president, in Maine: "When you win wars, troops come home." He said of Obama: "He's been completely wrong on the issue."

In Washington, the White House expressed displeasure with recent public comments by Iraqi leaders on the withdrawal question and suggested they might have the U.S. election on their minds. But the Iraqis stopped short of actual timetables or endorsement of Obama's pledge to withdraw troops within 16 months if he wins the presidency.

As Obama visited Iraq for the first time in more than two years, comments Monday by the government's spokesman roughly mirrored the Illinois senator's withdrawal schedule and offered a glimpse of Iraq's growing confidence as violence drops and Iraqi security forces expand their roles.

"We are hoping that in 2010 that combat troops will withdraw from Iraq," spokesman Ali al-Dabbagh said after Obama met with Prime Minister Nouri al-Maliki -- who has struggled for days to clarify Iraq's position on a possible timetable for a U.S. troop pullout.

Iraq's Sunni vice president, Tariq al-Hashemi, said after meeting Obama that Iraqi leaders share "a common interest ... to schedule the withdrawal of American troops."

"I'd be happy if we reach an agreement to say, for instance, the 31st of December 2010" would mark the departure of the last U.S. combat unit, he said -- then noted that any such goal could be revised depending on threats and the pace of training for Iraqi security forces. That date would be some seven months later than Obama's 16-month timeline.

Obama said almost nothing to reporters following him, but promised fuller impressions after he finishes here Tuesday and heads to Jordan and Israel.

He released a statement late Monday noting that Iraqis want a timeline "with a clear date" for the departure of U.S. combat forces.

"Prime Minister Maliki told us that while the Iraqi people deeply appreciate the sacrifices of American soldiers, they do not want an open-ended presence of U.S. combat forces. The prime minister said that now is an appropriate time to start to plan for the reorganization of our troops in Iraq -- including their numbers and missions. He stated his hope that U.S. combat forces could be out of Iraq in 2010," Obama said in a joint statement with Sens. Chuck Hagel, a Republican from Nebraska, and Jack Reed, a Democrat from Rhode Island, who accompanied him to the war zone.

The senators also acknowledged a significant decline in violence in Iraq, and said that while their has been some "forward movement" on political progress, reconciliation and economic development, there has not been "nearly enough to bring lasting stability to Iraq."

Obama told ABC News that military leaders have "deep concerns" about a timetable that doesn't account for changing conditions.

"I don't think that there are deep concerns about the notion of a pullout per se," he said in the interview. "There are deep concerns about, from their perspective, of a timetable that doesn't take into account what they anticipate might be some sort of change in conditions."

Obama also said that knowing what he knows now he still would have opposed sending more troops to Iraq last year.

In Washington, the White House expressed unhappiness about Iraqi leaders' apparent public backing for Obama's troop withdrawal plans and suggested they may be trying to use the U.S. presidential election as leverage for negotiations on America's presence and future obligations in the country.

"We don't think that talking about specific negotiating tactics or your negotiating position in the press is the best way to negotiate a deal," White House press secretary Dana Perino said after al-Maliki was quoted in a magazine article supporting Obama's proposed 16-month troop withdrawal timeline. Al-Maliki's spokesman, al-Dabbagh, initially appeared to try to discredit the magazine report but on Monday newly expressed hopes that U.S. combat forces could be out of Iraq by 2010.

The Bush administration has refused to set specific troop level targets but last week offered to discuss a "general time horizon" for a U.S. combat troop exit.

Asked whether the Iraqis might be trying to use the U.S. presidential election for leverage in negotiations over the future of the American military mission in Iraq, Perino said, "I think that a lot of other people look through the lens of a 2008 presidential election. ... Might they be? Sure. I mean, it's possible."

Iraq was the third leg of Obama's tour of the region, which has included stops in Kuwait and Afghanistan.

The counterpoint was clear: Obama opposed the Iraq war from the start and views the battle against the resurgent Taliban and al-Qaida in Afghanistan as America's most critical fight.

But Iraq is not the same place as when Obama last visited in January 2006.

Both Sunni insurgents, including al-Qaida in Iraq, and Shiite militias have suffered significant blows. And security forces in Baghdad -- once the scene of near daily car bombs and sectarian killings -- have made clear gains since last year's troop build-up of nearly 30,000 soldiers.

In an interview Monday on ABC's "Good Morning America," McCain said he hoped Obama would now "have the opportunity to see the success of the surge."

"This is the same strategy that he voted against, railed against," McCain said. "He was wrong about the surge. It is succeeding and we are winning."

All five surge brigades have left Iraq, but there are still about 147,000 U.S. soldiers in the country.

Obama -- traveling in a congressional delegation with Reed and Hagel -- first arrived in the city of Basra in Iraq's mostly Shiite south. Basra is the center for about 4,000 British troops involved mostly in training Iraqi forces. An Iraqi-led offensive begun in March reclaimed control of most of the city from Shiite militia believed linked to Iran.

Obama's foreign stops, which will conclude with a swing through Europe, were seen as an attempt to burnish his foreign policy credentials and address challenges by McCain that he is too inexperienced to lead in a time of war and global risks.

They also gave Obama a taste of some of the difficulties in Iraq that the next president will inherit. Important negotiations on a pact defining the future U.S. military commitment have stalled.