South Korean President Moon Jae In and his American counterpart Donald Trump welcomed the resumption of inter-Korean talks, with Mr Trump saying that the United States is also open to talks with the regime "at an appropriate time and circumstance".
In a phone conversation last night, both leaders agreed the talks on Tuesday may go beyond North Korea's participation in the upcoming Winter Olympics and naturally lead to negotiations about denuclearisation.
Mr Moon credited the high-level talks to Mr Trump's firm principles and cooperation, and both agreed there was a need to maintain a firm stance for the success of any dialogue, South Korea's presidential office said in a statement.
Mr Trump also gave an assurance that the US would not take any military action against the North while talks are ongoing.
The two leaders spoke hours after Mr Moon had addressed the North-South talks - the first in two years - during a televised New Year press conference.
He welcomed them, but warned that his country would continue to work with the international community to apply pressure on the North to give up nuclear weapons.
He stressed there was a need to build on the talks to improve inter-Korean ties and pursue peace on the Korean peninsula.
"The denuclearisation of the Korean peninsula as declared by the two Koreas (in the past) is our fundamental position that can never be compromised," he told a pool of 200 local and foreign journalists.
Noting that his goal was to prevent another war, Mr Moon said he would not seek immediate reunification with the North, but was open to a summit with Pyongyang if "conditions are met".
The two Koreas agreed on Tuesday to revive military talks, in what is being seen as a step forward in easing tensions triggered by a string of missile and nuclear tests by Pyongyang in the past two years.
North Korea also agreed to a big delegation to the Olympics of 400 to 500, comprising officials, athletes and cheer squads.
South Korea's Foreign Ministry had indicated it would consider lifting some sanctions temporarily to facilitate the North's attendance in the Games, to be held from Feb 9 to 25 in the alpine county of Pyeongchang.
But Mr Moon ruled this out yesterday, saying Seoul would keep pace with the international community on the issue of sanctions.
South Korea's unilateral sanctions on the North include a ban on new economic exchanges and the closure of the joint Kaesong industrial complex.
Some experts say North Korea's peace overture is a trap meant to drive a wedge between Seoul and Washington, and to elicit economic concessions from Seoul to tide the regime over tough times resulting from sanctions.
But Mr Moon said a two-track approach of engagement with pressure would bring about a virtuous circle. "At the end of the day, improving ties with the North is inevitably linked to resolving the nuclear crisis," he said.
Analysts said Mr Moon's cautious stance towards North Korea is meant to silence critics, and to appeal to a wider majority of conservatives who are wary of his liberal government's North-friendly policies.
Sogang University international relations professor Kim Jae Chun told The Straits Times: "Many people worry that the Moon Jae In government will fall into the trap North Korea set up, so it is important to emphasise that denuclearisation is something he can't give up."
By giving credit to his US counterpart, Mr Moon has sent the signal that "South Korea is on the same page as the Trump administration", said Professor Kim.
Yesterday's press conference marked Mr Moon's first since his election last May. He also pledged to remain committed to "people-centred" economic growth and to make the issue of youth unemployment a national priority.