U.S. President Donald Trump said Tuesday his meeting with North Korean leader Kim Jong Un next month may not take place as scheduled amid growing concern that Kim may be reluctant to abandon nuclear weapons.

"There's a very substantial chance that it won't work out," Trump said in a meeting with South Korean President Moon Jae In at the White House, part of which was open to the media. "It may not work out for June 12."

Trump said preparations are continuing toward a June 12 summit in Singapore, but that the meeting -- which would be the first ever between a sitting U.S. president and a North Korean leader -- could be postponed unless "certain conditions" are met.

He made the remarks in reference to a sudden change in the North's posture last week when it threatened to call off a Trump-Kim summit if Washington demands "unilateral nuclear abandonment" by Pyongyang.

Trump said he detected a shift in Kim's tone after the North's leader met Chinese President Xi Jinping on May 7-8 in China, and suspected Xi may be influencing Pyongyang's approach toward Washington.

"There was a somewhat different attitude after that meeting, and I'm a little surprised," he said. "I don't like that...I can't say I'm happy about it."

(Donald Trump says his summit with Kim Jong Un may not happen June 12.)

The U.S. leader also accused Beijing of easing restrictions on trade with North Korea through their border in what would be a violation of U.N. sanctions on Pyongyang.

"It has been cut off, largely. But it's been opened up a little bit lately," he said. "I don't like that."

Trump said Kim will be safe and happy and his country will be rich if the two leaders strike a deal on denuclearization.

"North Korea has a chance really to be a great country," he said. "And I think they should seize the opportunity and we'll soon find out whether or not they want to do that."

The Trump-Moon meeting came after Trump indicated last Thursday that he will provide Kim with security assurances in return for denuclearization.

Trump assured Kim that he will "get protections that will be very strong," saying the North's leader will not suffer the same fate as former Libyan leader Muammar Gaddafi if he gives up his nuclear weapons.

Gaddafi, who agreed to abandon his nascent nuclear weapons program in the early 2000s, was overthrown and killed after a North Atlantic Treaty Organization-led coalition intervened in support of an uprising in the northern African country in 2011.

[All photos Getty/Kyodo]

U.S. Secretary of State Mike Pompeo has said American businesses could invest in energy and agriculture in North Korea and help develop infrastructure in the cash-strapped country if it achieves a complete, verifiable and irreversible denuclearization.

During a meeting between Moon and Kim on April 27 -- seen as a prelude to the Trump-Kim summit -- the two Koreas pledged to work for the "complete denuclearization" of the Korean Peninsula.

But there was an abrupt change in tone from Pyongyang last week. North Korea unilaterally suspended high-level talks with South Korea, blaming U.S.-South Korea military exercises that Pyongyang said are a rehearsal for invasion.

Pyongyang also warned that if Washington insists on demanding that North Koreans abandon their nuclear weapons before receiving any benefits, it "cannot but reconsider our proceeding" to the Trump-Kim summit.

Kim has sought "phased and synchronous measures," an incremental, action-for-action process in which North Korea secures concessions such as sanctions relief for each move it takes toward denuclearization.

But Trump has pledged to maintain maximum pressure and sanctions until Pyongyang denuclearizes. He said he will not repeat the mistakes of past administrations, asserting they gave North Korea too many concessions despite the country not abandoning its nuclear arsenal and infrastructure.