(CNN) -- Sens. John McCain and Barack Obama engaged in a pointed exchange over al Qaeda in Iraq on Wednesday.
Sen. John McCain questioned Sen. Barack Obama's way of handling the war in Iraq.
McCain questioned whether Obama was aware of the al Qaeda base. Obama's response was: "There was no such thing as al Qaeda in Iraq until George Bush and John McCain decided to invade Iraq."
McCain was in Tyler, Texas, and Obama was in Columbus, Ohio.
"I understand that Sen. Obama said that if al Qaeda established a base in Iraq that he would send troops back in militarily. Al Qaeda already has a base in Iraq. It's called al Qaeda in Iraq," McCain said.
"It's a remarkable statement to say that you would send troops back to a place where al Qaeda has established a base -- where they have already established a base."
McCain's comments come in response to remarks Obama made Tuesday night in a debate with Sen. Hillary Clinton. He was asked if the president would have the right to go back into Iraq in order to suppress an insurrection after downsizing the U.S. troop presence. Watch what Clinton and Obama said about the war »
"I always reserve the right for the president ... to make sure that we are looking out for American interests," Obama said. "And if al Qaeda is forming a base in Iraq, then we will have to act in a way that secures the American homeland and our interests abroad."
A statement by McCain's press office Wednesday said, "Is Sen. Obama unaware that al Qaeda is still present in Iraq, that our forces are successfully fighting them every day, and that his Iraq policy of withdrawal would embolden al Qaeda and weaken our security?"
Obama responded to the latest attacks from McCain, saying his comments were taken out of context.
Obama said the question he was asked during the debate was a "big hypothetical."
"I said, 'Well, I would always reserve the right to go in and strike against al Qaeda if they were in Iraq,' so you know, this is how politics works," Obama said at a rally in Columbus.
"McCain thought that he could make a clever point by saying ,'Well let me give you some news Barack, al Qaeda is in Iraq,' like I wasn't reading the papers, like I didn't know what was going on."
"I said, 'Well first of all, I do know that al Qaeda is in Iraq. That's why I've said we should continue to strike al Qaeda targets. But I have some news for John McCain, and that is that there was no such thing as al Qaeda in Iraq until George Bush and John McCain decided to invade Iraq."
Obama continued to blast Bush and McCain, saying, "John McCain may like to say he wants to follow Osama bin Laden to the gates of hell, but so far all he's done is follow George Bush into a misguided war in Iraq."
McCain in his statement said "the Democratic presidential contenders deny progress and see only gloom and doom. Where is the audacity of hope when it comes to backing the success of our troops all the way to victory in Iraq? What we heard last night was the timidity of despair."
The latest exchange comes as a new poll suggests McCain would pose a tough match for the eventual Democratic nominee.
Obama is the front-runner for the Democratic nomination. Clinton trails by 97 delegates, but 370 delegates are up for grabs next Tuesday. Watch the shift in Clinton-Obama dynamics »
According to a Los Angeles Times/Bloomberg poll, McCain would be in tight races with either of the remaining Democratic presidential candidates.
McCain is statistically tied with Obama, 44 percent to 42 percent, and ahead of Clinton by 6 points, 46 percent to 40 percent.
The poll's margin of error was plus-or-minus 3 percentage points.
The poll also showed McCain with a 61 percent approval rating, a number higher than both Clinton's and Obama's in past polls.
The Arizona senator holds a clear advantage on dealing with the war in Iraq, according to the poll, and holds a 9 point advantage on economic issues over Obama, despite having acknowledged that area is not his expertise. E-mail to a friend
CNN's Chris Welch and Alex Mooney contributed to this report.