BAGHDAD -- Face to face with Iraq's leaders, Barack Obama gained fresh support yesterday for the idea of pulling all U.S. combat forces out of the war zone by 2010. But the Iraqis stopped short of actual timetables or endorsement of Obama's pledge to withdraw American troops within 16 months if he wins the presidency.

The Democratic presidential contender also got a briefing from the top U.S. commander in the region, Gen. David Petraeus, and he met with a few of the nearly 150,000 U.S. troops in Iraq in the war's sixth year.

Back in the U.S., Republican rival John McCain said he hoped Obama's visit would open his 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.

Comments yesterday by the nation's government 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.

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 as he walked to and from his meetings, promising to give fuller impressions after his stop in Iraq wraps up.

In Washington, the White House expressed unhappiness about the Iraqi leaders' public statements on troop withdrawal plans and suggested the Iraqis may be seeking leverage in 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," press secretary Dana Perino said after al-Maliki was quoted in a magazine article supporting the 16-month troop withdrawal timeline.

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, she 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."

Important negotiations on a pact defining the future U.S. military commitment have stalled.

American diplomats hoped to reach a final accord by the end of the month, but it now seems the goal is a stopgap "bridge" document that would maintain the status for U.S. forces once a U.N. mandate on their presence expires at the end of the year.