The likely GOP nominee told an audience Thursday: "We have drawn down to pre-surge levels. Basra, Mosul and now Sadr City are quiet."

Obama responded: "That's not true and anyone running for commander-in- chief should know better."

In fact, U.S. troop levels are not yet down to levels before President Bush's troop increase last year, a strategy shift McCain had pushed for some four years before the president authorized it.

There were 15 combat brigades in Iraq before the increase began. Five were added, and the United States has been reducing numbers since December. As of Friday, there are 17 brigades in Iraq, another brigade will depart in June and the plan is to pull out another in July, returning the level to 15.

Prior to the increase, there were 130,000-135,000 U.S. troops in Iraq. As of this week, that number was 155,000, and the Pentagon plans to drop that to 140,000 by the end of July.

The McCain campaign blamed a parsing of verb tense and semantics. But McCain, himself, insisted Friday that he didn't misspeak.

"Of course not. I said we've drawn down," the top Republican on the Senate Armed Services Committee said at a news conference. "The rest of them will be home at the end of July."

He added: "We have drawn down, we will continue to draw down and I hope that General Petraeus will see fit to recommend for the consideration of the president of the United States an additional draw down after the end of July."

Obama seized on McCain's insistence that he didn't misspeak. "Today, Sen. McCain refused to correct his mistake," Obama said in remarks prepared for a rally Friday in Great Falls, Mont. "Just like George Bush, when he was presented with the truth, he just dug in and refused to admit his mistake."

McCain tried to turn the tables on Obama, reading a quote from October 2007 in which Obama said he thought that the increase strategy would exacerbate sectarian violence. Top U.S. commanders have credited the force increase with helping curb violence.

"Clearly, Senator Obama made exactly the wrong judgment about whether the surge would succeed in Iraq," McCain said. "He has no fundamental understanding of the entire situation that warranted the surge."

McCain's comments—and Democratic criticism of them—continued a week of haggling over the Iraq war with Obama, who is expected to clinch the Democratic nomination. The war is certain to be a major issue in the general election because McCain advocates a continued troop presence in Iraq but Obama calls for a withdrawal.

A Vietnam prisoner of war, McCain relishes a debate on national security, his strength, in a difficult election year for Republicans. Obama, a first-term Illinois senator, meanwhile sees an opening on the war, given that most of the public now opposes it.

Both have been arguing that the other lacks the judgment to be commander in chief.

McCain points to Obama's limited foreign policy experience, and this week, he questioned Obama's two-year-absence from Iraq. Obama, who said he was considering a trip to Iraq, questions whether McCain is fit to lead on Iraq. Obama's campaign points to what they call McCain's too-rosy assessments of the war, a previous gaffe over the difference between Sunnis and Shiites—and, now, his troop-level comment.

Democrats pounced on it early Friday, with Obama's campaign arranging a conference call with two high-profile surrogates.

Wisconsin Gov. Jim Doyle, an Obama supporter, argued that McCain was misrepresenting the facts when he said that the U.S. military has drawn back to levels before last year's force increase in Iraq. "That just is just not true. And everybody knows it's not true. And I assume Senator McCain just doesn't know the facts here," Doyle said in a conference call with reporters.

Massachusetts Sen. John Kerry, another Obama backer, echoed Doyle's criticism.

That prompted a pointed response from the McCain campaign.

"Clearly John Kerry and Barack Obama have very little understanding of troop levels, but considering Barack Obama hasn't been to Iraq in 873 days and has never had a one-on-one meeting with General Petraeus, it isn't a surprise to anyone that he demonstrates weak leadership," the McCain campaign said.

Obama rejected a McCain proposal for a joint trip to Iraq by the candidates. "He's been proposing a joint trip to Iraq that's nothing more than a political stunt. He's even been using it to raise a few dollars for his campaign," Obama said in Montana. "It seems like Sen. McCain's a lot more interested in my travel plans than the facts."

In a dueling conference call, Sen. Jon Kyl, a McCain proponent, accused the Obama campaign of deflecting attention from what Kyl called the real issue that Obama still calls for withdrawal even though the troop-influx strategy has curbed the violence and he hasn't been to Iraq in two years. Said Kyl: "It is correct that the levels of troops there are not the same as they were during the surge, and, in fact, all of them will be home by the end of July."

Said Randy Scheunemann, McCain's senior foreign policy adviser: "The difference is so minuscule that I'm not sure it rises to the level of nitpicking."

Later Friday, Obama responded: "I don't think tens of thousands of American troops amounts to nitpicking."

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