In an apparent shot at Christie, Paul says Sunday "there's room for people who believe in bigger government in our party." The New Jersey governor is considered a moderate whose views on government spending differ sharply from the libertarian Paul's.
The two men, potential rivals for president in 2016, have been sparring for weeks.
Paul told "Fox News Sunday" that Republicans should concentrate growing the party instead of bickering. He said the GOP "is shrinking almost down to nothing" in the Northeast, Christie's home base, and needs people with new ideas to attract independents and Democrats.