Republican presidential candidate Chris Christie on Wednesday morning fired back at GOP primary rival Sen. Rand Paul (Ky.) for saying a no-fly zone in Syria could spark a global war -- responding by stating that one has already started.

"The problem for folks like Senator Paul is they don't realize we're already in World War III. The fact is that this is a new world war and it won't look like the last two," Christie said on CBS's "This Morning" Wednesday. "If he doesn't understand that we're already in that war, then it's just another example of why he's so unfit to be president of the United States."

Paul sharply denounced Christie's position during Tuesday night's fifth GOP debate in Las Vegas, calling his advocacy for a no-fly zone dangerous and comparing him to former secretary of state Hillary Clinton.

"Well, I think if you're in favor of World War III, you have your candidate," Paul said Tuesday. "My goodness, what we want in a leader is someone with judgment, not someone who is so reckless as to stand on the stage and say, 'Yes, I'm jumping up and down; I'm going to shoot down Russian planes.'"

Paul added that although he disapproves of Russia's efforts on behalf of Syrian President Bashar al-Assad, declaring a no-fly zone when "Russia already flies in that airspace" would represent a serious lapse in judgement.

Highlights from CNN's Republican presidential debate on Dec. 15 in less than two minutes. (Sarah Parnass/The Washington Post)

Christie on Wednesday questioned Russia's commitment to fighting the Islamic State, knocking President Obama and former secretary of Clinton for their diplomatic efforts.

"We know how Russian troops in Crimea, we have them disrupting Ukraine," Christie said. "They are aligning with the Iranians to try to create and Iranian empire across the Middle East. I don't call that a friend."