WASHINGTON (CNN) -- Sens. Barack Obama and John McCain on Wednesday continued their fight over how to prosecute detainees held at the U.S. naval base in Guantanamo Bay, Cuba.
A recent Supreme Court ruling that gives Guantanamo detainees greater legal rights has ramped up the debate, and the McCain and Obama campaigns sent out their surrogates early Wednesday to pick up where they left off Tuesday.
Rudy Giuliani, a former Republican presidential candidate and McCain supporter, and Susan Rice, an Obama campaign foreign policy adviser, took turns jabbing at the opposing camp on CNN's "American Morning."
The firestorm started when Obama on Monday praised last week's Supreme Court ruling to put Guantanamo Bay detainees on trial, pointing to how the 1993 World Trade Center bombers were prosecuted.
McCain's team on Tuesday charged that Obama is delusional and naive for his views on how to track terror suspects and how to handle them if they're caught.
"Sen. Obama is a perfect manifestation of a September 10th mind-set. He brings the attitude, the failures of judgment, the weakness and the misunderstanding of the nature of our adversary, and the dangers posed by them, to a series of policy positions," said Randy Scheunemann, a McCain foreign policy adviser.
McCain has said the Supreme Court's ruling must be honored, but he disagrees with giving those rights to detainees, saying they are "unlawful combatants."
Obama on Wednesday defended his terrorism policy positions.
"Yesterday, Sen. McCain showed yet again that the addition of continuing George Bush's policies is not where he offers similarities, he's also going to use the Bush-Cheney political playbook that's based on fear. He put a bunch of staunch Iraq war supporters on the phone to accuse me of having a 'pre-9/11 mind-set,' " he said.
Obama went on to say that he believes that he's "very clear about the threats America faces ... and I think, in fact, it's the failed policies of the Bush administration and the unwillingness to look towards the future that is causing us so many problems around the world." Watch more on the terrorism debate »
Obama made the comments after his first meeting with his Senior Working Group on National Security, a group of senior Democrats who are foreign policy and national security veterans.
The Obama campaign says the presumptive Democratic presidential nominee will consult with this group on a regular basis between now and the November election. See a full list of Obama's national security team
Later Wednesday, Obama gathered with nearly 40 retired admirals and generals to discuss the state of the nation's armed forces and the challenges that the U.S. military faces in hot spots around the world.
Meanwhile, Giuliani responded Wednesday to Obama's stance on trying terrorists in U.S. courts. In a conference call, Giuliani said the "real problem is his having said that in essence, the 1993 situation was really correctly handled by its being a criminal prosecution."
"The reality is it wasn't over with in 1993; it led to several other serious attacks on Americans, and then, of course, the catastrophic attack of September 11," he added.
Giuliani also criticized Obama for applauding the Supreme Court ruling to extend habeas corpus rights to Guantanamo detainees.
"I do not understand why at a time that we're facing this terrorist threat, we want to create new rights that didn't exist before for people who are alleged to be involved in terrorism or who are alleged to be enemy combatants," Giuliani said.
Giuliani also responded to words from Sen. John Kerry. The Obama supporter suggested Tuesday that Osama bin Laden would have habeas corpus rights if he were captured and sent to Guantanamo. Giuliani called the statement "startling."
"The reality is there seems to be more concern about the rights of terrorists or alleged terrorists than the rights the American people have to safety and security," he said.
Rice responded: "What Rudy Giuliani and the McCain campaign are doing is straight out of the Karl Rove playbook. It's distorting, dishonest attacks that bear no semblance to reality. This administration and John McCain have for seven years pursued a stupid and fundamentally failed policy as we try to deal with the war on terrorism." Watch Rice defend Obama's position »
"First of all, we'll try to kill Osama bin Laden. But if Osama bin Laden or anybody else is captured, we have to deal with that very forcefully," Rice later added. "The way you deal with it is not to hold somebody in violation of our Constitution, indefinitely in detention and never convict them."
But some decisions on those trials may end up in the hands of the next president.
"Given the pace we've been going, there is no doubt that the fate of Khalid Sheikh Mohammed and the fate of Guantanamo will not be in President Bush's hands, but in his successor's hands," said Jeffrey Toobin, CNN senior legal analyst.
And McCain and Obama have conflicting views on how to handle them.
The military tribunal system, established by law in 2006, provides less openness to the public and fewer rights for suspects than a normal court.
McCain supports the system, although he'd like to change the venue.
"I would declare the closure of Guantanamo Bay and move those prisoners to Fort Leavenworth, Kansas, and proceed with tribunals," he said January 6.
Obama voted against the tribunal system and has vowed to scrap it.
"As president, I will close Guantanamo, reject the Military Commissions Act and adhere to the Geneva Conventions. Our Constitution and our Uniform Code of Military Justice provide a framework for dealing with the terrorists," Obama said in 2007.
An Obama aide says he wants to try the suspects publicly in existing courts.
Analysts say it all adds up to an uncertain road ahead -- dependent on who is elected president.
CNN's Ed Hornick, Alexander Marquardt and Brian Todd contributed to this report.