President Moon Jae-in held a summit with his US counterpart, Donald Trump, in Washington on Thursday in their first talks since the breakdown of the Hanoi summit between the US and North Korea in February.

The two leaders reaffirmed close coordination toward the shared goal of completely denuclearizing the Korean peninsula and establishing permanent peace.

The governing DP said the allies reaffirmed the shared goal of North Korea's denuclearization based on their firm alliance.

"The two nations shared the understanding that top-down diplomacy is essential for the peace-making process (on the Korean Peninsula) and signaled that this approach will be viable down the road," DP spokesman Lee Hae-sik said in a statement.

Lee said the DP will foster cooperation to help Moon serve as a broker and facilitator between the US and the North in resolving Pyongyang's nuclear issue.

But the LKP likened the summit result to something like a "drifting cloud."

"(Before the summit), the government signaled the US may accept its 'good enough deal,' but the result was totally different," LKP floor leader Na Kyung-won said at a meeting with party officials.

In the wake of the breakdown of the Hanoi summit, South Korean officials raised the need for a "good enough deal" to achieve "early harvest" in the lengthy process of the North's denuclearization. The US voices for a "big deal" that includes detailed denuclearization steps.

The minor opposition Bareunmirae Party welcomed the summit as an occasion to reaffirm Seoul and Washington's decades-long alliance.

But it also added the allies confirmed differences over specific ways to denuclearize North Korea and the scope of sanctions reliefs.

"South Korea apparently faces the task of playing a proper role (as a facilitator) while gauging to what extent it would take into account the US stance," the third-largest party said.

The minor liberal Party for Democracy and Peace assessed that the Moon-Trump summit will help revive stalled talks between the US and North Korea.

The leftist Justice Party hoped the latest summit could pave the way for the two Koreas to hold a summit as early as possible. (Yonhap)