President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE on Tuesday said his planned summit with North Korean leader Kim Jong Un may not take place in June, raising further doubt about whether the historic meeting would occur.

“There’s a very substantial chance that it won’t work out, and that’s OK,” Trump told reporters in the Oval Office. “That doesn’t mean it won’t work out over a period of time, but it may not work out for June 12.”

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Trump spoke during a meeting with South Korean President Moon Jae-in, whose government has helped broker nuclear diplomacy between the U.S. and North Korea. Moon’s visit comes three weeks before the scheduled Trump-Kim summit in Singapore.

Moon said the “fate and the future” of the Korean Peninsula depend on the talks. South Korea has urged Trump to resolve the nuclear crisis with Kim through talks.

But North Korea threw the nuclear summit into doubt last week when it scrapped high-level talks with South Korea and threatened to pull out of the talks with Trump if the U.S. continues to demand unilateral denuclearization.

North Korean officials also lashed out at Trump’s national security adviser, John Bolton, who suggested a North Korean arms deal could follow a “Libya model.”

Libyan leader Moammar Gadhafi in 2003 surrendered his nuclear and chemical weapons in exchange for sanctions relief, but eight years later, was toppled by NATO-backed rebel forces.

Trump said Kim is “serious” about denuclearization and stressed that the North Korean leader's safety would be ensured under any deal that eliminates his nuclear weapons.

“We will guarantee his safety,” Trump said, adding that if the U.S. and North Korea strike a deal, Kim would “be very proud” of what he did for his country.

The president also suggested North Korea’s neighbors would be willing to boost economic assistance efforts under a proposed deal.

“South Korea, China and Japan ... they will be willing to help, and I believe invest very, very large sums of money to make North Korea great,” he said.

But Trump attributed North Korea's harder line to a trip Kim took to China earlier this month in the run-up to the summit.

“There was a little change in attitude from Kim Jong Un,” he said.

The president also urged Chinese President Xi Jinping to remain committed to his goal of denuclearizing the Korean Peninsula, expressing hope it could influence Kim to remain willing to enter negotiations.

"I think that President Xi is a world-class poker player,” Trump said. "I can't say that I'm happy about it."

--Updated at 1:50 p.m.