"The most urgent issue is to make sure the United States and North Korea will engage in talks", Chung said, as he departed with National Intelligence Service chief Suh Hoon.
The South Korean envoys were expected to brief US officials on North Korea's stance on possible future talks with Washington and its apparent willingness to suspend nuclear tests if the security of the North's government is assured.
Trump, who last fall told Secretary of State Rex Tillerson he was "wasting his time" trying to talk with the North, tweeted Tuesday that "possible progress" had been made in North Korea's capital and that all sides were making serious efforts.
"Me", he joked, before crediting USA -led sanctions that, with China's help, are punishing North Korea's economy.
"There has been a lot of news on that today, he said referring to the news coming from the region that North Korea is willing to talk with the US".
The government urged North Korea Wednesday to act toward denuclearization following Tuesday's announcement of an agreement to hold an inter-Korean summit next month.
US and South Korean officials worry that North Korea will ultimately lay down impossible demands in talks - such as the complete withdrawal of USA forces from South Korea - and once diplomacy fails, emerge as an even greater threat than before. "We call on the parties, particularly the United States and the DPRK, to engage in dialogue sooner rather than later", he said.
Little is known about the delegations' visit to the United States, including who they'll be meeting with and what they'll be telling their allies about the North Korea meeting.
When asked if he believes "the North Koreans are prepared to give up their nuclear weapons?" he replied: "We're going to see".
"I think that's been a factor, but the sanctions have been very, very strong, and very biting".
Some of that work can be done on the ground, although a live test will eventually be needed as North Korea has never flown a missile at a trajectory that would simulate a long-range flight, experts say.
If this fails to cause North Korea to change its ICBM missile testing, Trump stated "we'll have to go to Phase 2", which would be a "rough thing. very, very unfortunate for the world". He also is set to travel to the border with South Korea for a summit meeting in late April with the South's president, Moon Jae-in.
New Delhi has been cutting back on trade with North Korea but has maintained diplomatic links.
Japan's prime minister warned today that North Korea's offer of denuclearisation talks with the United States could be a ploy to play for time and stressed the need for Pyongyang to take "concrete" steps.