John McCain, fighting back against what he says are Barack Obama's distortions of his position on Iraq, turned the tables on his potential Democratic opponent Tuesday by asking Obama to explain his plans for a "strike force" in the area.

Obama has campaigned vigorously on his pledge to pull troops from Iraq. On Monday, he said he wouldn't abandon the Mideast in the process of ordering a withdrawal.

"What I said was I would have a strike force in the region, perhaps in Iraq, perhaps outside Iraq so we could take advantage of or we could deal with potential problems that might take place in the region," Obama said. "That's very different from saying we'd have a permanent occupation in Iraq. And it's certainly different from saying we would have a high level of combat troops inside Iraq for a decade or two decades or, as John McCain said, perhaps 100 years."

McCain, the likely Republican presidential nominee, responded Tuesday that he'd like to know how many troops make up a "strike force."

"Where are they based? What do they do? Now I'm intrigued. He has said he will pull out all troops before. How do you reconcile those two?" McCain asked.

McCain and Obama have been sparring for weeks over a continued U.S. presence in Iraq. McCain has said he would be OK with the U.S. maintaining troops in Iraq for 100 years. Obama has portrayed those remarks as saying McCain is willing to wage war in Iraq for 100 years.

McCain first uttered the comments in question during a January town hall meeting in New Hampshire, saying he'd be fine with a long-term U.S. commitment in Iraq.

"President Bush has talked about our staying for 50 years, maybe 100. We've been in Japan for 60 years, in South Korea for 50 years or so. That would be fine with me as long as Americans are not being injured or harmed or killed," McCain said at the time.

Obama said Monday that McCain, a Navy aviator and Vietnam prisoner of war, is a war hero, but he is just wrong on Iraq.

"John McCain wants to continue a war in Iraq perhaps as long as 100 years," Obama said during a town hall meeting in Lancaster, Pa.

"John McCain is willing to sign up for the prospect of spending as much as $150 billion or more each year for who knows how long," Obama added, noting that by suggesting that the U.S. keep a long-term presence in Iraq, "that implies that there is some criteria by which we would understand how long it takes. John McCain has not been clear about what exactly leads him to decide it's time to pull out."

But the non-partisan group Factcheck.org says Obama's claim that McCain wants 100 years of war in Iraq is a distortion to the point of "rank falsehood. "

On Tuesday, McCain repeated his argument of a day earlier that Obama's claims demonstrate the Democrat's fundamental misunderstanding of U.S. foreign policy. In those comments, McCain said Obama clearly has no understanding of military history in the U.S. and how this country projects its spheres of influence.

"We fought a war with Japan and Germany. Afterwards we maintained a military presence there, which we are doing today. We fought a war in Korea, we maintained a military presence in Korea, which we are doing to this day. The first Gulf War, we threw Saddam Hussein out of Kuwait, and we have a military presence there to this day," McCain told reporters aboard his campaign plane.

"So he doesn't either, hasn't read or understand ... the history of this country in warfare, and the way that we secure alliances and secure the peace. That's through military government to government agreements that call for United States presence and mutual defense. Not only in that country itself, but also in the region. ... So in all due respect, it displays a fundamental misunderstanding of history and how we've maintained national security, and what we need to do in the future to maintain our security in the face of the transcendent challenge of radical Islamic extremism. And I understand that because he has no experience or background in any of it," McCain said.

Obama did acknowledge that the U.S. has been in South Korea and has maintained other commitments for extended periods, and he suggested that it's not unusual for U.S. troops to be stationed abroad to protect embassies and American diplomats.

McCain backers call that acknowledgment proof that Obama is knowingly twisting McCain's words, and aides Obama's remarks are an example of politics as usual.

FOX News' Carl Cameron, Jake Gibson and Mosheh Oinounou contributed to this report.