"The situation on the Korean Peninsula changed dramatically after President Trump held a meeting with Chairman Kim Jong-un on June 12 last year," Moon said at the start of his meeting with Trump at the White House.

The meeting between Moon and Trump came after Trump's second summit with Kim in Hanoi ended without a nuclear deal, also prompting an apparent stall in US-North Korea talks on ending the North's nuclear ambition.

Moon said the Hanoi summit was part of a process to reach a greater agreement.

"I believe what is important now is to maintain the momentum of dialogue, and offer an outlook to the world that a third North Korea-US summit will be held in the near future," Moon added, according to pool reports.

Trump said he may have failed to achieve all he wanted to in the Hanoi meeting but that certain things were very good.

The US president also said he wished to continue holding dialogue with the North Korean leader.

"It could happen," Trump said when asked about the possibility of his third summit with North Korea's Kim.

"I enjoy the summit. I enjoy being with the chairman and it really is a productive and it really is a step by step," he added.

Many believe the Hanoi summit collapsed due to a gap between Washington and Pyongyang over when and what the North would get in return for its denuclearization.

Trump appeared to remain opposed to providing any interim rewards to North Korea.

"In the right time I would have a great support. This isn't the right time, but in the right time I'd have a great support," he said when asked whether he would support the resumption of inter-Korean economic cooperation.

Whether the North would be entitled to early rewards was expected to be a key discussion point in the Moon-Trump summit.  

The South Korean president has voiced the need to provide the impoverished North with some carrots that he says would only encourage the country to further accelerate its denuclearization process.

Following their one-on-one meeting the leaders of South Korea and the US were joined by their key aides and officials in a small group meeting, which will be followed by an expanded summit over lunch.

Moon arrived here Wednesday on a two-day visit. He is set to head home later Thursday.