WASHINGTON, June 17 (Reuters) - Republican John McCain's camp accused Democratic presidential rival Barack Obama on Tuesday of being weak on terrorism, drawing a sharp rebuke from Obama on the politically charged issue of how to deal with Islamic extremists.

In an exchange reminiscent of the 2004 U.S. presidential campaign, McCain's advisers pounced on Obama for saying terrorism suspects could be treated as criminals "within the constraints of the Constitution."

They said his comments reflected a dangerous failure to understand the threat posed by terrorism.

"We have seen that Senator Obama is a perfect manifestation of a September 10th mindset," McCain adviser Randy Schuenemann said. The comment echoed Karl Rove, the former political adviser to President George W. Bush, who in 2006 accused Democrats of a "pre-9/11" world view.

"He brings the attitude, the failures of judgment, the weakness and the misunderstanding of the nature of our adversaries," Schuenemann said.

The Illinois senator quickly fired back, saying Republicans had little standing to criticize him on the issue.

"These are the same guys who helped engineer the distraction of the war in Iraq at a time when we could have pinned down the people who actually committed 9/11," Obama said on his campaign plane.

"What they're trying to do is to do what they've done every election cycle, which is to use terrorism as a club to make the American people afraid," Obama said.

McCain and Obama will face off in November's presidential election. McCain, a former Navy pilot and Vietnam prisoner of war, has stressed national security and tried to paint Obama as too inexperienced to be trusted as commander in chief.

ECHO OF 2004

In the 2004 campaign, Bush questioned Democrat John Kerry's approach to battling terrorism and accused him of being soft on the issue because he said he would treat terrorists as regular criminals.

Obama set off the exchange in an ABC News interview on Monday night, when he contrasted the indefinite detention of Guantanamo Bay detainees with the criminal prosecution of the 1993 World Trade Center bombers.

"Let's take the example of Guantanamo. What we know is that in previous terrorist attacks, for example, the first attack against the World Trade Center, we were able to arrest those responsible, put them on trial. They are currently in U.S. prisons, incapacitated," Obama said in the interview.

"And the fact that the administration has not tried to do that has created a situation where not only have we never actually put many of these folks on trial, but we have destroyed our credibility when it comes to rule of law all around the world," he said.

The campaigns sponsored dueling conference calls with advisers from each side trading accusations on the issue.

Kerry participated in the Obama call and said McCain was "the candidate of the Iraq war mindset, a mindset that completely misunderstands and dangerously underestimates the threats of the 21st century."

Former New York Mayor Rudolph Giuliani, who won a reputation for strong leadership after the Sept. 11 attacks in the city, said in a statement Obama "appears to believe that terrorists should be treated like criminals -- a belief that underscores his fundamental lack of judgment regarding our national security."

Obama said the Republican strategies of 2004 would not work in 2008.

"I'm looking forward to having a robust argument about these situations," he said. "I don't shy away from it. The way these issues have been framed have done a great disservice to America." (Additional reporting by Caren Bohan; Editing by Doina Chiacu) (For more about the U.S. political campaign, visit Reuters "Tales from the Trail: 2008" online at

blogs.reuters.com/trail08/

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