Sen. Marco Rubio, R-Fla., says North Korean leader Kim Jong Un is putting on a "show" for the world in talks with the U.S., China, and South Korea, but will "never" denuclearize.

"I remain convinced that he does not want to denuclearize, in fact, he will not denuclearize. But he wants to give off this perception that he is this open leader, he is peaceful, he is reasonable, and that's why you see they basically stopped talking to us for two weeks," Rubio told ABC's "This Week" on Sunday.

[White House: Trump 'not naive' on North Korea's denuclearization claims]

Rubio, who is a member of the Senate Foreign Relations Committee, said Kim has an "emotional and a personal, psychological attachment" to his nuclear weapons" because they make him feel "prestigious."

The Florida lawmaker supported Trump's Thursday decision to cancel the June 12 summit in Singapore with Kim. In explaining his move, Trump cited threatening public remarks from the authoritarian nation's leaders. The summit, announced earlier this year, was aimed at denuclearization of the Korean Peninsula.

Since the cancellation, the North Koreans have softened their rhetoric, expressing an openness to salvage the meeting, and Kim held a surprise meeting with South Korean President Moon Jae-in on Saturday inside the the Demilitarized Zone between their two nations.

In the preceding weeks, North Korea released three American detainees and blew up a nuclear testing site in what was meant as a show of good faith to the U.S.

However, Rubio remains unimpressed. He said Kim is doing just enough to toy with the U.S. and remove sanctions imposed on his country.

"It's all a show. It's a show," Rubio said. "The facilities he blew up was a testing site. They can test it anywhere. They don't have to have a town hall meeting in North Korea to decide whether to test weapons."

As the tone has improved in recent days, the White House sent officials part of a pre-advance team for Singapore left as scheduled to prepare should the summit take place. Late Saturday evening, Trump told reporters at the White House as he met with Joshua Holt, an American captive just released from Venezuela, that talks to reinstate the summit with Kim have gone "very well."

Despite the signs of improvement, Rubio claimed Kim's behavior is erratic, stemming from deeper issues not related to the U.S.

"He has to figure out how to survive in power for 50-something years as a dictator and is probably afraid if he gets rid of the weapons at some point, someone will take him out," Rubio said. But Kim's on-again, off-again interest in negotiating with the State Department will eventually prompt Trump to draw a line in the sand, he added.

"If you don't think that you are going to be able to reach a deal where he gives up his missiles and gives up his nukes, then you are going to have to make a decision, where we have been the whole time. 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?" Rubio asked.

"And if you are not, then you are going to have to do something to go after him at some point. I'm not in favor of that. It's not something I relish or take lightly," he said.

Trump as a presidential candidate touted himself as a deal-maker who can improve diplomatic relations with other countries. Guest host Martha Raddatz appeared skeptical that the businessman had the toolbox to handle a dictator, but Rubio said Trump is giving Kim a taste of his own medicine and may be making progress.

"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 and large, has unbalanced, basically left the North Koreans off balance, and they are normally the ones doing the dramatic action and this sort of unpredictable action that set everybody off. The president has given him a taste of his own medicine," Rubio said.

"It's a style we have never seen in a presidency before, but it seems to have at least, you know, knocked them off of I can imagine they for all these years, North Korea has been used to dealing with traditional politicians and I give the president credit for that," he added. "That may be what sets the conditions, but ultimately there has to be a deal, and it has to be verifiable."