(CNN) - Sen. Rand Paul labeled New Jersey Gov. Chris Christie a "moderate" on Tuesday, hours after the governor described himself as a "conservative."
"I think the Republican Party is a big party, and we need moderates like Chris Christie who can win in New Jersey," Paul said on CNN's The Situation Room with Wolf Blitzer.
"What that means about the national party, I'm not sure there's an answer. But we do need moderates like Chris Christie in the party."
Christie and Paul, both considered potential 2016 presidential candidates, engaged in a back-and-forth earlier this year over ideology versus pragmatism in the Republican Party.
Paul, of Kentucky, argued Tuesday he thinks the GOP is generally "more conservative" than Christie, suggesting the governor has a tough road ahead if he decides to seek the 2016 Republican presidential nomination.
"I think it will be more difficult - states like Iowa are very conservative," Paul said. "South Carolina is very conservative. New Hampshire, I think, is conservative with a little bit of a libertarian bent."
Christie was considered as a potential running mate by Mitt Romney's campaign last year, but he has since fallen out of favor with some in the conservative base for praising President Obama after Superstorm Sandy and sometimes taking more establishment GOP positions on issues involving national security.
Asked earlier Tuesday if he considers himself more of a moderate or a conservative, Christie told CNN's Jake Tapper, "I'm a conservative."
"I've governed as a conservative in this state, and I think that's led to some people disagreeing with me in our state, because it's generally a left-of-center, blue state," he said.
"The difference has been is I haven't tried to hide it, or mask it as something different," Christie added.
For his part, Paul argued Tuesday the GOP needs to be a "broader party in many ways," saying "I welcome (Christie) to the party and think he's an important part of it."
- CNN's Ashley Killough contributed to this report.
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