Rand Paul seemed to change his position on outlawing private discrimination Thursday.

After several media appearances in which Paul said the government should not prohibit private businesses from discriminating on the basis of race, the Kentucky Republican seemed to backtrack in an interview this afternoon.

CNN's Wolf Blitzer asked Paul whether Woolworth's department store should have been allowed to continue separating blacks from whites at its lunch counter in the 1960s.

"I think that there was an overriding problem in the South so big that it did require federal intervention," Paul replied. 

Paul clarified earlier Thursday that, despite his criticism of portions of the legislation, he would have voted for the Civil Rights Act had he been in Congress at the time.