Edwards, a former North Carolina senator and the 2004 Democratic nominee for the U.S. vice presidency, drew Republican ire last month when he dubbed U.S. President George W. Bush's "war on terror" a "bumper sticker."
Former New York mayor Giuliani has focused his campaign on his image as a strong leader after the September 11 attacks destroyed the city's World Trade Center towers.
Edwards dismissed criticism of his "bumper sticker" comment as rhetoric aimed at presenting Bush critics as unpatriotic.
"If Mayor Giuliani believes that what President Bush has done is good and wants to embrace it and run a campaign for the presidency saying 'I will give you four more years of what this president has given you,' he's allowed to do that.
"He'll never be elected president of the United States, but he's allowed to do that," he said.
"America is looking for something different. They want us to be tough ... but they expect us to be smart," he said.