U.S. President Donald Trump suggested Tuesday that his planned meeting with North Korean leader Kim Jong-un may not happen next month.

Trump met with South Korean President Moon Jae-in at the White House ahead of the historic summit set for June 12 in Singapore.

"There's a chance that it will work out. There's a very substantial chance it won't work out," Trump said at the top of his talks with Moon. "That doesn't mean it won't work out over a period of time. But it may not work out for June 12. But there's a good chance that we'll have the meeting."

This photo shows South Korean President Moon Jae-in (L) meeting with U.S. President Donald Trump at the White House in Washington on May 22, 2018. (Yonhap)

Preparations for the summit continue, but it could be canceled if U.S. conditions aren't met, he added.

North Korea has threatened to pull out of the summit over U.S. demands for "unilateral" denuclearization. The Trump administration maintains that its aim is the complete, verifiable and irreversible dismantlement of North Korea's nuclear program, with no promise of concessions until that process is in motion.

Trump said North Korea's denuclearization must take place, and while the summit may not happen June 12, it could still take place later.

"I do think he's serious. I think he would like to see that happen," Trump said of Kim's willingness to give up his nuclear weapons program.

He acknowledged the difficulty of getting North Korea to dismantle the program all at once without offering concessions.

"It would certainly be better if it were all in one. Does it have to be? I don't think I want to totally commit myself," he said. "You do have some physical reasons that it may not be able to do exactly that. So for physical reasons, over a very short period of time."

Again the U.S. president assured the North Korean leader of his "safety" in exchange for complete denuclearization, indicating he has no plans to remove Kim from power.

"He will be safe. He will be happy," Trump explained. "His country will be rich. His country will be hardworking and very prosperous. They're very great people. They're hardworking, great people."

Trump also offered the North investment from South Korea, China and Japan to help make that country "great."

The two Koreas could eventually reunify, he added, but for now, it's unclear whether Moon will meet with Kim again after their first summit on the inter-Korean border last month. Moon agreed then to visit Pyongyang in the fall.

Trump again appeared to blame Chinese President Xi Jinping for Kim's sudden threat to cancel the June meeting, saying Xi is a world class poker player. He especially cited Kim's second visit to China, earlier this month, after which Trump said he sensed a shift in attitude.

China has been a key player in the U.S.-led sanctions campaign against Pyongyang. As North Korea's only major ally and trading partner, China has significant leverage over the wayward nation but also has an interest in keeping the North as a buffer against U.S.-allied South Korea.

Trump has hinted that Beijing could be using its influence with Pyongyang as a bargaining chip in trade negotiations with the U.S.

Washington has underscored that Trump agreed to meet with Kim at the latter's invitation in March. Trump has also said he will walk away from the summit if it doesn't prove fruitful.

North Korea recently released three American prisoners in a goodwill gesture ahead of what would be an unprecedented U.S.-North Korea summit. U.S. Secretary of State Mike Pompeo flew to Pyongyang to bring them home and meet with Kim for a second time to fine-tune preparations for the summit.

Sen. Lindsey Graham (R-SC) said Sunday that Trump wants to end the North Korean threat during his current term, which ends in early 2021, and will likely resort to military action should diplomacy fail.

Trump also appeared to issue a veiled threat last week, saying the North will meet the same fate as Libya's toppled regime only if it doesn't strike a deal with the U.S.

Moon, who took office a year ago, has vowed not to allow war on the peninsula again.

In his meeting with Kim last month, the two agreed to pursue "complete denuclearization" and a formal end to the 1950-53 Korean War within the year. The conflict ended in an armistice, not a peace treaty, leaving the sides technically at war.

More than 28,000 American troops are stationed in the South to deter North Korean aggression, and Trump has been reported to be considering a reduction of the military presence as part of a potential nuclear deal with the North.

Trump has said he will not discuss the issue at the summit. And his press secretary, Sarah Sanders, told reporters after the Moon-Trump talks that the troops issue did not come up between them.

"I have great confidence in your president," Trump said in response to a South Korean reporter asking about the U.S. president's level of trust in Moon's role as a mediator between Washington and Pyongyang. "I think he's a very capable person. I think he's an extremely competent man. I think he's a very good person."

At the press briefing, Sanders also said she expects the issue of North Korea's human rights abuses to be raised and addressed between Trump and Kim.

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