Sen. Rand Paul (R-Kentucky). AP Photo/John Locher At the CNN Republican presidential debate on Tuesday night, Sen. Rand Paul of Kentucky suggested that his rival Chris Christie would start World War III if elected president.

Paul was asked to respond to Christie, the New Jersey governor, saying he would implement a no-fly zone in Syria and be willing to order the shooting down of Russian planes that violate it.

"I think if you're in favor of World War III, you have your candidate," Paul said, gesturing to Christie.

"What we want in a leader is someone with judgment," Paul added, "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 continued, saying the US needed to confront Russia "from a position of strength," not a "point of recklessness that would lead to war."

Paul also got in a dig about the Bridgegate controversy, for which three former government officials linked to Christie faced charges. Court documents showed that David Wildstein, a longtime Christie ally and former Port Authority executive, was involved in a scheme to punish a political rival by ordering lane closings on the George Washington Bridge in September 2013.

"When we think about the judgment of someone who might want World War III, we might think about someone who might shut down a bridge because they don't like their friends," Paul said.

Christie shot back, seeming to attack Democratic front-runner Hillary Clinton.

"I'll tell you what reckless is," Christie said. "What reckless is is calling Assad a reformer."

Earlier in the debate, Christie noted that Clinton had previously called Syrian President Bashar Assad a "reformer." In 2011, she said "many of the members of Congress of both parties who have gone to Syria in recent months have said they believe [Assad] is a reformer."