Watch Giuliani's interview from American Morning.
(CNN) – Former New York City Mayor Rudy Giuliani accused Barack Obama of "a softer and more defensive approach to terrorism," while Obama's foreign policy advisor Susan Rice called John McCain's stance on the issue "stupid and fundamentally failed," in separate interviews Wednesday on CNN's "American Morning."
This morning's back-and-forth between the two presidential campaigns was a continuation of a disagreement over how to prosecute detainees held at Guantanamo Bay that began earlier this week.
The firestorm started when Obama on Monday praised last week's U.S. Supreme Court ruling to put Guantanamo Bay detainees on trial, pointing to how the 1993 World Trade Center bombers were prosecuted.
"The real problem is his having said that in essence the 1993 situation was really correctly handled by it being a criminal prosecution," Giuliani said on a conference call with reporters shortly after the CNN interview. "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."
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," said Giuliani.
Rice not only aimed her fire at McCain, but Giuliani as well.
"What Rudy Giuliani and the McCain campaign are doing is straight out of the Karl Rove play book," she said in the CNN interview. "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."
She later added, "First of all, we'll try to kill Osama bin Laden. But if Osama bin Laden or anybody else is captured, we have deal with that very forcefully. The way you deal with it is not to hold somebody in violation of our constitution, indefinitely in detention and never convict them."