The rapid-fire, long-distance exchange Wednesday underscored that the two consider each other likely general election rivals, even though the Democratic contest remains unresolved.
McCain criticized Obama for saying in Tuesday night's Democratic debate that, after U.S. troops were withdrawn, as president he would act "if al-Qaida is forming a base in Iraq."
"I have some news. Al-Qaida is in Iraq. It's called `al-Qaida in Iraq,'" McCain told a crowd in Tyler, Texas, drawing laughter at Obama's expense. He said Obama's statement was "pretty remarkable,"
Obama quickly answered back while campaigning in Ohio. "I do know that al-Qaida is in Iraq and that's why I have said we should continue to strike al-Qaida targets," he told a rally at Ohio State University in Columbus.
"But I have some news for John McCain," Obama added. "There was no such thing as al-Qaida in Iraq until George Bush and John McCain decided to invade Iraq. ... They took their eye off the people who were responsible for 9/11 and that would be al-Qaida in Afghanistan, that is stronger now than at any time since 2001."
Obama said he intended to withdraw U.S. forces from Iraq "so we actually start going after al-Qaida in Afghanistan and in the hills of Pakistan like we should have been doing in the first place."
While he praised McCain as a war hero and saluted his service to the country, Obama said the Arizona Republican was "tied to the politics of the past. We are about policies of the future."
Noting that McCain likes to tell audiences that he'd follow Osama bin Laden to the "gates of hell" to catch him, Obama taunted: "All he (McCain) has done is to follow George Bush into a misguided war in Iraq."
McCain said he had not watched Tuesday night's Democratic presidential debate but was told of Obama's response when asked if as president he would reserve the right to send U.S. troops back into Iraq to quell an insurrection or civil war.
Obama did not say whether he'd send troops but responded: "As commander in chief, I will always reserve the right to make sure that we are looking out for American interests. And if al-Qaida is forming a base in Iraq, then we will have to act in a way that secures the American homeland and our interests abroad."
On Wednesday, Obama expanded slightly that he "would always reserve the right to go in and strike al-Qaida if they were in Iraq" without detailing what kind of strike that might be — air, ground or both.
'I will not surrender'
Throughout the primary season, McCain has repeatedly attacked Obama and Hillary Clinton for saying they would withdraw troops from Iraq.
"And my friends, if we left, they (al-Qaida) wouldn't be establishing a base," McCain said Wednesday. "They'd be taking a country, and I'm not going to allow that to happen, my friends. I will not surrender. I will not surrender to al-Qaida."
He said that withdrawing troops would be "waving the white flag."
In the debate, Clinton did not answer the question about re-invasion of Iraq on grounds it contained "lots of different hypothetical assessments."
For years, McCain has urged sending more troops into Iraq, even before President Bush adopted such a strategy about a year ago.
"I knew enough from talking to the men and women who are serving that this new strategy was what we needed, and I'm telling you, it is succeeding," McCain said. "So what needs to happen, we need to continue this strategy. It should be General Petraeus' recommendation, not that of a politician running for higher office, as to when and how we withdraw."
He was referring to Gen. David Petraeus, the top American commander in Iraq.
As he began a swing through President Bush's home state, which holds a presidential primary election on Tuesday, McCain made sure to play up a line he always uses: "I also think it might be nice for President Bush to get a little credit that there's not been another attack on the United States of America," he said to applause.
Both Obama and Clinton campaigned in Ohio on Wednesday. Obama was heading later in the day for at least three days of campaigning in Texas.