ⓒYONHAP News

President Moon Jae-in held talks with U.S. President Donald Trump at the White House on Thursday, seeking to find a breakthrough in the stalled nuclear talks.

"I believe that the Hanoi summit is not actually, was not a source of disappointment but it has actually the parts of a big--bigger process that will lead us to a bigger agreement. So, the important task that we face right now is to maintain the momentum of dialogue and also express a positive outlook regarding the third U.S.-North Korea summit and to the international community that this will be held in the near future."

However, Trump is lukewarm about pushing for a third summit with Kim anytime soon.

"It could happen. A third summit could happen. And it’s step by step. It’s not a fast process; I’ve never said it would be. It’s step by step."

Trump also said he will maintain the sanctions on North Korea.

"No, we want sanctions to remain in place. And frankly I had the option of significantly increasing them I didn't want to do that because of my relationship with Kim Jong-un... We could always increase them but I didn't want to do that at this time."

He also told reporters that now is not the right time to support Seoul's push for the resumption of the joint inter-Korean industrial complex and other cross-border projects.

After the talks which lasted for about two hours, South Korean presidential national security adviser Chung Eui-yong told reporters that Moon shared his plan to revive U.S.-North Korea dialogue via an inter-Korean summit.

"The two leaders agreed that the top-down method is essential in the Korean Peninsula peace process... President Moon explained his plans to hold an inter-Korean summit in the near future and reaffirmed his intentions to hold close consultations with President Trump so that another North Korea-U.S. summit can serve as a milestone in the denuclearization of North Korea."

Trump asked Moon to inform him of the North's position as soon as Seoul finds out.

Moon's two-day stay in Washington comes after Trump's second summit with Kim in late February ended without an agreement.

After wrapping up one of his briefest overseas diplomatic engagements, Moon left for Seoul. He is set to arrive home on Friday night Korea time.