The timing of the announcement coincides with the election of South Korea's new president Moon Jae-in and comes amid a continued dispute between Beijing and Washington over the deployment of a Terminal High Altitude Area Defense (THAAD) anti-missile system on South Korean soil. "If needed, I will fly immediately to Washington". I will go to Beijing and I will go to Tokyo.
Beijing has been upset by the installation of USA missile-defense system in South Korea that was approved by Moon's conservative predecessor as a hedge against North Korea.
At home, Mr Moon begins his term facing multiple challenges, including the aftermath of the huge corruption scandal that saw his conservative predecessor Park Geun Hye impeached.
Calling Pyongyang's atomic weapons programme a "a hard problem that can be solved", Trump invited Moon to visit the United States "as early as possible", according to the statement.
"I will make a just, united country", Moon told a crowd gathered just before midnight to see the former human rights lawyer who entered politics to lead a party just five years ago.More news: Spurs overcome Leonard injury, Harden to beat Rockets in OT
Analysts say Moon will need to act quickly in naming key security and foreign policy aides and ministers in order to ease geopolitical tensions.
But this would put South Korea at odds with the United States, where President Trump has vowed to use "maximum pressure" to force the North to give up its nuclear weapons program, and with an global community that is largely supportive of tougher sanctions.
"President Moon said he understands China's interest in the THAAD deployment and its concerns, and said he hopes the two countries can swiftly get on with communication to further improve each other's understanding", Yoon told a briefing.
On North Korean problems, Abe said he hopes to closely cooperate with Moon in denuclearizing the Korean Peninsula.
A phone conversation between Moon and US President Donald Trump on Wednesday night also touched on the Korean Peninsula.More news: Joanna Jedrzejczyk on Jessica Andrade and Aiming for UFC Flyweight Title
"It hasn't much to do with THAAD directly, but it is a kind of warning" to South Korea and the U.S., Song Zhongping, a Chinese military affairs expert and commentator for Hong Kong's Phoenix TV, told the Associated Press.
Moon later spoke with Japanese Prime Minister Shinzo Abe and agreed a bilateral meeting soon.
The five tasks are: implementing the 1991 "Basic Agreement in reconciliation, non-aggression and exchanges and cooperation between the South and the North"; desirability of the United States and Japan improving and normalising relations with North Korea; all nations in the world, including the four countries (the US, Japan, Russia and China) whose interests intersect on the Korean peninsula, should interact with North Korea so as to make it a responsible member of the worldwide community; eliminating weapons of mass destruction from the Korean peninsula; and changing the Armistice Agreement of 1953 that brought the Korean War to a halt (not an end) into a peace regime. But Moon said during the campaign that he will re-evaluate whether to extend the agreement based on its effectiveness.
Beijing also has its own issues with Seoul.More news: Kellyanne Conway says James Comey's own actions led to his firing