Republican Sen. Marco Rubio, a member of the Senate Foreign Relations Committee, said he is convinced that North Korea will not give up its nuclear program and that its release of U.S. prisoners and other gestures are "a show."

Rubio told ABC News Chief Global Affairs Correspondent and "This Week" Co-Anchor Martha Raddatz on Sunday that the U.S. will have to make a decision on whether it can live with North Korea's having nuclear weapons that could put America at risk.

"Ultimately I remain convinced that [North Korean leader Kim Jong Un] does not want to denuclearize; he will not denuclearize, but he wants to give off this perception that he's this open leader, that he's peaceful, that he's reasonable," the Florida senator told Raddatz.

“It’s all a show," Rubio said. Kim "released three Americans that were innocently there, blew up a facility that was probably already damaged ... Here’s the bigger point, the facility he blew up was a testing site. He can test [weapons] anywhere."

Raddatz asked the Florida senator about a recent tweet about the North Korean leader in which he said US “options to deal with him are narrowing.”

Rubio responded, “If you don't think you're ever going to be able to reach a deal where he gives up his missiles and gives up his nukes then you're going to have to make a decision, which is where we've been the whole time, and that is, 'Are you prepared to live in a world where someone like him possesses not just nuclear weapons, but the ability to hit the mainland of the United States?' And, if you're not, then you're going to have to do something to go after them at some point."

On President Trump’s strategy for summit talks, Rubio gave the president credit for keeping North Korea “off balance.”

“I think President Trump is trying to figure out how to get this guy to a negotiating table so they can negotiate… and I think his strategy by large has unbalanced, basically left the North Koreans off balance,” Rubio said. “They are usually the ones that out there doing this sort of dramatic action and -- and you know this sort of unpredictable action that set everybody off. The president has given him a taste of his own medicine.”

“I give the president credit for that, but ultimately, there’s got to be a deal,” Rubio added. “That is a very difficult thing to accomplish with a country in North Korea that has no history of diplomacy, no history of negotiations, and no one around that’s ever done this before.”