Jake Tapper, host of CNN's State of the Union, asked Kasich on Sunday if the recent terror attacks in San Bernardino were a sign that it was time to block gun purchases for people on the government's no-fly and terrorist watch lists.

Kasich said that he would consider a moratorium on gun purchases for those on the no-fly list, but he argued that it was a bad idea to block suspected terrorists from buying firearms.

"When our law enforcement stops somebody that's on the watch list, we don't tell them they are on the watch list," he explained. "We want to make sure we can exploit all the information that we can possibly get."

"So, if all of the sudden you tell everybody that's on the watch list that you can't do this or that then guess what happens? Then we lose our ability to track, we lose our ability to gather information," he added. "So I think we have to be careful."