Washington (CNN) President Donald Trump on Thursday said US and North Korean officials are continuing to prepare for a scheduled diplomatic summit next month, even as Pyongyang threatened in recent days to pull out of what would be a historic first meeting between a North Korean leader and US president.

Trump also reassured Kim Jong Un the North Korean leader would remain in power if he abandons his nuclear weapons program, but warned Kim that North Korea could be "decimated" if he refuses to strike a deal with the US.

Trump's comments were his most extensive since North Korea dealt a blow to hopes for a successful US-North Korea summit next month in a series of statements earlier this week.

"They've been negotiating like nothing happened," Trump said of North Korea.

While he has read news reports about the North Korean statements and spoken with the South Koreans, Trump said the North Koreans have yet to signal plans to cancel the summit.

"If the meeting happens, it happens. And if it doesn't, we go on to the next step," Trump said. "We may have the meeting. We may not have the meeting. If we don't have it, that will be very interesting. ... We'll see what happens."

Libya model

The President did seek to distance himself from a comment by his national security adviser, John Bolton, that had irked the North Koreans, dismissing talk of applying the "Libyan model" to the denuclearization of North Korea and reassuring Kim he will remain in power if he gives up his nuclear weapons.

But the President also appeared to be confused about what "Libyan model" Bolton referred to late last month, when his national security adviser said the "Libya model of 2003, 2004" could be applied to US negotiations with North Korea.

Bolton was referring to the dismantling of Libya's weapons of mass destruction program, but Trump appeared to refer to the "Libyan model" as the subsequent military intervention in Libya years later that removed Moammar Gadhafi from power.

"The Libyan model isn't a model that we have at all when we're thinking of North Korea," Trump said. "This with Kim Jong Un would be something where he would be there. He would be running his country. His country would be very rich."

"The Libyan model was a much different model. We decimated that country. We never said to Gadhafi, 'Oh, we're going to give you protection,' " he continued. "We went in and decimated him, and we did the same thing with Iraq."

Drawing on those comments, Trump also warned Kim of the alternative to striking a denuclearization deal: the decimation of North Korea and Kim's removal from power.

"That model would take place if we don't make a deal," Trump said.

Still willing

The President noted that North Korea's harsher tone this week came after Kim met for the second time with Chinese President Xi Jinping, and suggested the Chinese leader could be "influencing" Kim to harden his stance.

While Trump wavered on whether the summit would go forward next month, he made clear that he remains willing to meet with his North Korean counterpart. The question, he said, is whether Kim is still willing.

"You have to want to do it. With deals ... you have to have two parties that want to do it," Trump said. Kim "absolutely wanted to do it. Perhaps he doesn't want to do it."

Trump still plans to meet with South Korean President Moon Jae-in next week, as part of preparations for the Kim summit.

For its part, North Korea said it would not communicate with the South until the two sides can resolve differences over joint US-South Korea military drills.

"It will not be easy to sit back with South Korea's current 'regime' unless the serious situation that suspended the high-level inter-Korean talks is resolved," Ri Son Gwon, North Korea's chairman of the Committee for the Peaceful Reunification, said in a state media report. "The direction of future North-South relations will depend solely on the actions of the South Korean authorities."

Bolton conferred Wednesday morning with his South Korean counterpart, who offered little clarity on North Korea's intentions. He, along with other administration officials, said they believed the summit would still proceed as planned.

"We want to do whatever we can to make the meeting a success," Bolton told Fox News Radio. "But there should be no mistake that if we don't see that commitment to denuclearization then we're not going to make the mistakes of past administrations and fall into endless discussions with North Korea."