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

The Democratic presidential contender also got a military briefing — and a helicopter tour — from the top U.S. commander in the region, Army Gen. David Petraeus, and 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.

As Obama visited Iraq for the first time in more than two years, comments yesterday 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 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."

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

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

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