WASHINGTON (CNN) -- Former New York City Mayor Rudy Giuliani sharply criticized fellow presidential candidate John Edwards Wednesday, saying that the former North Carolina senator's renunciation of the term "War on Terror" is evidence Democrats are in "denial."

"When you go so far as to suggest that the global war on terror is a bumper sticker or slogan, it kind of makes the point that I've been making over and over again," Giuliani told Fox News on Wednesday night. "That the Democrats, or at least some of them, are in denial."

In a speech before the Council on Foreign Relations in New York City Wednesday, Edwards said, "The war on terror is a slogan designed only for politics, not a strategy to make America safe. It's a bumper sticker, not a plan."

Giuliani's comments echo controversial remarks he made on the campaign trail in New Hampshire last month, when he said that if a Democrat is elected president, America would likely suffer "more losses" due to terrorism.

Shortly after that comment, Edwards said Giuliani was "divisive and just plain wrong."

In March, Giuliani himself said he did not like the term "War on Terror," telling reporters it allows enemies to redefine the United States incorrectly as a nation that prefers war.

"We kind of have to get it into our mentality and into our policies and stop sort of feeding the idea that this is a war of our choice," said Giuliani, calling it a mistake to coin the phrase.