(CNN) - Sen. Rand Paul said Sunday that Gov. Chris Christie is making a mistake when he argues the GOP needs to be more pragmatic and hold fewer internal ideological debates.
"Saying there's no room for us is a big mistake," Paul said on "Fox News Sunday."
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The New Jersey governor made headlines Thursday when he said in a speech at the Republican National Committee's summer meeting that the GOP "is not a debating society."
"We are a political operation that needs to win," he said.
While Christie didn't mention Paul's name specifically, his remarks were interpreted as the latest round in the back-and-forth between the two potential presidential candiates that seems to represent a broader divide between establishment and more libertarian-leaning Republicans.
"I think we have some folks who believe that our job is to be college professors," Christie said. "Now college professors are fine, I guess. Being a college professor, they basically spout out ideas that nobody does anything about. For our ideas to matter we have to win. Because if we don't win, we don't govern."
But Paul argued Sunday there was enough space in the party "for both of us."
"It's big enough for a lot of different Republicans," he said. "That's how we grow our party. Libertarian Republicans like myself care about the right to privacy. We care about a more moderate, less aggressive foreign policy."
"The party in the Northeast is shrinking, almost down to nothing," he added, repeating a line that he has used before. "They need to be looking to people with new and different ideas who attract youth, independents and even Democrats to our party." Paul represents Kentucky.
Paul's father, former Rep. Ron Paul of Texas, quickly hit back at Christie's remarks Thursday afternoon, saying on CNN's "The Situation Room" that the New Jersey governor "offers nothing."
Asked Sunday if he agreed with his father, Rand Paul didn't weigh in on the three-time presidential candidate's comments.
"There's room for people who believe in bigger government in our party, and I think some of the things that (Christie) seems to have promoted make us believe that, well, he thinks that there's a lot more spending that could go on," Paul said.
- CNN's Peter Hamby contributed to this report.