Kasich -- a primary opponent of Trump's -- wrote 2008 GOP nominee John McCain's name at the top of his ballot. Meanwhile, House Speaker Paul Ryan, who has already followed through on his pledge to cast his vote for Trump, failed to mention the candidate by name during a Fox News interview Tuesday, instead referring to Trump only as "our nominee."

"I'm not happy with either John Kasich or Paul Ryan, particularly John Kasich," Santorum told CNN's Brooke Baldwin.

Santorum, a GOP presidential candidate in 2012 and 2016, continued to call out Kasich, rebuking him for his public disdain for the Republican presidential candidate.

"If you're watching, John, you signed a pledge," he said. "You signed a pledge saying that you would support the Republican nominee for president. You signed a pledge in order to get on the ballot in South Carolina. You promised that you would follow through with that. You knew Donald Trump had a chance because he was leading in the polls at the time to be our nominee and you signed it anyway."

"You can't say a man who's not going to keep his word is someone that, frankly, should be paid attention to when it comes to how he's going to vote. John, you are better than that," he continued.