President Donald Trump laid out a stark choice for North Korea's Kim Jong Un ahead of their planned summit next month: Abandon nuclear weapons and be rewarded with "protections," or risk being overthrown and possible death if the arsenal remains.

Trump maintained the scheduled June 12 meeting in Singapore is on track, despite the North's threat Wednesday to cancel over concerns about the U.S. push to see the complete denuclearization of the Korean Peninsula.

The North has argued it needs its nuclear weapons to preserve its security, and has expressed concerns about giving up its nuclear program. The North cites the example of former Libyan leader Moammar Gadhafi, who died at the hands of rebel forces amid a popular uprising in October 2011; he had given up his nuclear program in the 2000s.

National Security Adviser John Bolton explicitly cited "the Libya model of 2003-2004" as a basis for the North Korea talks last month, which drew personal rebuke from the North Korean government Wednesday.

Trying to address the North Korean concerns, the president said if Kim were to agree to denuclearize, "he'll get protections that would be very strong."

But Trump warned that failure to make a deal could have grave consequences for Kim. Mentioning what happened in Libya, Trump said, "That model would take place if we don't make a deal."

"The Libyan model isn't the model we have at all. In Libya we decimated that country." Trump added. "There was no deal to keep Gadhafi."

Trump said he is "willing to do a lot" to provide security guarantees to Kim. "The best thing he could do is make a deal."

Trump also suggested China was influencing North Korea's thinking regarding the summit, pointing to Kim's visit to China immediately before Secretary of State Mike Pompeo visited Pyongyang last week to finalize the summit date and location.

Trump said Thursday that nothing has changed with respect to North Korea after the warning from Pyongyang. He said North Korean officials are discussing logistical details about the meeting with the U.S. "as if nothing happened."

In addition to threatening to pull out of the meeting with Trump, the North abruptly canceled a planned meeting with South Korean officials over joint U.S.-South Korean military exercises.

Pentagon spokeswoman Dana White said Thursday that the schedule of military exercises hasn't changed. She added the annual exercises are long-planned, defensive in nature and meant to ensure the readiness of U.S. and South Korean forces.

Exercise Max Thunder began Monday and concludes May 25. It includes aircraft from across the U.S. military services. Last year's exercise included roughly 1,200 U.S. personnel and about 640 South Koreans. This year's drill is similar.

Speaking at an Oval Office meeting with NATO Secretary-General Jens Stoltenberg, Trump also said he will not discuss U.S. troop levels in South Korea during his meeting with Kim.

The North has said it won't return to talks with Seoul due to the exercises.

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Associated Press writer Ken Thomas contributed to this report.