Perkins endorsed Santorum in January, along with a group of other leaders of socially conservative organizations.

He told CNN that evangelical voters are "not comfortable with [Romney] on his policies." He said religious voters tolerated Romney when he looked like the inevitable nominee, "but now they see a viable option" in Santorum, who continues to challenge Romney in the polls and has snatched the vote from him in more states than Gingrich.

On Wednesday, influential conservative blogger Erick Erickson announced "it is time for Newt Gingrich to exit" on his blog. He said Gingrich's failure to win the vote in either Alabama or Mississippi on Tuesday — two Southern states where he campaigned hard after declaring that the South would be his key to victory — "proved he is neither a regional candidate nor a spoiler."

Erickson wrote, "I still think Romney is the nominee. But I think Santorum vs. Romney one on one gives Romney a run for his money he needs to become a candidate conservatives can potentially rally around."

Conservative news magazine National Review called on Gingrich to drop out and endorse Rick Santorum last month.

"He could be a kingmaker if he stepped out of the race and threw his support to another candidate," Perkins said in his statement this week.

Gingrich has resisted calls to drop out so far, and maintained that he will stay in the race until the GOP convention in late August.