US President Donald Trump has said his summit with North Korean leader Kim Jong-un “may not work out” in June, raising further doubt about whether the historic meeting would occur as planned.

Trump made the comment during a meeting with South Korean President Moon Jae-in in the Oval Office of the White House on Tuesday.

“We’re moving along. We’ll see what happens,” Trump told reporters. “There are certain conditions we want to happen. I think we’ll get those conditions. And if we don’t, we won’t have the meeting.”

The US president did not specify the conditions Washington was setting for the landmark meeting due in Singapore on 12 June.

“There is a very substantial chance that it won’t work out, but that’s OK,” he added. “It doesn’t mean it won’t work out over a period of time, but it may not work out for June 12. But there is still a good chance we’ll have the meeting.”

US President Donald Trump gestures as he welcomes South Korea's President Moon Jae-in in the Oval Office of the White House in Washington, US, May 22, 2018. (Photo by Reuters)

The South Korean president, for his part, expressed optimism about the occurrence of the planned summit between Trump and Kim, and said he was “confident” that the meeting between the two sides would be a success.

“We are looking forward to the first US-North Korea summit and we find ourselves standing one step closer to the dream of achieving the complete denuclearization of the Korean peninsula and world peace,” Moon said.

“I have no doubt that you will be able to complete and accomplish an historic feat that no one has been able to achieve in the decades past,” he added.

During the Tuesday talks in the Oval Office, Trump said he believed the North Korean leader was "absolutely very serious" about denuclearization and stressed that Kim’s safety would be guaranteed under any deal that eliminated his nuclear weapons.

Pyongyang threatened last week to scrap plans for what would be a historic meeting between Trump and Kim in Singapore on June 12 over US pressure on the North.

North Korea not only threatened to cancel the unprecedented summit with Washington but also suspended a high-level meeting with Seoul after South Korea conducted joint military drills with the US on the Korean Peninsula.

The talks were supposed to discuss implementing a declaration issued at the end of an April 27 inter-Korea summit, which included interest in the “common goal” of denuclearization.

South Korea has vowed to mediate talks between the United States and North Korea.

Washington and Pyongyang have no diplomatic relations. The US has imposed many rounds of sanctions on North Korea, has substantial military presence near the country, and has numerously threatened to invade it over its weapons programs.

Trump has previously suggested the Demilitarized Zone separating North and South Korea would be the best place for the high-stakes summit, but American officials had asked him to hold the talks in a third country.

Singapore has diplomatic relations with both the United States and North Korea.

The Trump-Kim summit, if it takes place, would mark the first such meeting between a sitting US president and a North Korean leader in history.