South Korea's top politicians on Monday hailed the latest meeting between US President Donald Trump and North Korean leader Kim Jong-un for providing a crucial momentum for advancing the stalled nuclear talks and peninsula peace efforts.

Trump and Kim agreed Sunday to restart working-level nuclear negotiations in a few weeks during their impromptu meeting in the Demilitarized Zone (DMZ) that divides the two Koreas. Trump became the first sitting US president to step into the North and invited Kim to visit the White House.

The event was broadly welcomed in South Korean political circles even from the conservative main opposition Liberty Korea Party, which is critical of President Moon Jae-in's efforts to reconcile with the North and mediate between Washington and Pyongyang.

"President Trump mentioned a comprehensive agreement and announced working-level negotiations would begin within two to three weeks. This is a good sign for breaking the deadlock in the nuclear talks," LKP chief Hwang Kyo-ahn said during a meeting of the party's leadership council.

He said working-level talks between the two sides would face difficulties as the North is resorting to its traditional salami tactics, which separates issues and makes new demands for progress every step of the way.

"If President Moon wants to be a true middleman, his priority should be persuading North Korea to change its attitude," Hwang added.

He urged Moon to set a clear goal of the complete denuclearization of the North and closely cooperate with the United States.

Lee Hae-chan, chairman of the ruling Democratic Party, said the three leaders "set another milestone toward peace on the Korean Peninsula" through their unprecedented meeting at the border village of Panmunjom inside the DMZ.

"The US president stepped on North Korean soil for the first time in 66 years after the armistice and what was expected to be a brief meeting became a de facto third US-North Korea summit," Lee said during a party leaders' meeting.

"Though there was no prior agreement, the meeting could be arranged so quickly because there was trust among the leaders of the two Koreas and the United States on the basis of a strong South Korea-US alliance," he added.

Chung Dong-young, chairman of the minor liberal Party of Democracy and Peace, said the next summit between Trump and Kim could occur within this year, possibly in August or September.

In a radio talk show, the former unification minister said: "Kim Jong-un needs to produce some results within the year and so does Trump. I think the fourth US-North Korea summit is possible within this year." (Yonhap)