They were given the undisclosed message on Monday when meeting Mr Kim in rare talks in Pyongyang, local media say.
It is not clear whether the envoys will meet US President Donald Trump.
Previous US talks with North Korea have come to nothing and there has been no comment from Pyongyang itself.
It has also been agreed that the two Koreas’ leaders will meet at a summit in April for the first time in more than a decade, and the first since Mr Kim took power.
South Korea’s head of national security Chung Eui-yong and intelligence agency chief Sun Hoon met North Korea’s reclusive leader during a two-day trip that ended on Tuesday.
Mr Kim clearly expressed his country’s willingness to talk with Washington and to pause weapons testing while this happens, Mr Chung told reporters on Tuesday.
“We cannot reveal everything to the media but we do have additional views of North Korea we will relay to the United States when we visit the US,” he said, according to South Korean news agency Yonhap.
Donald Trump responded cautiously to news that North Korea is willing to talk about giving up its nuclear weapons.
South Korean officials have been vague and careful with their diplomatic language following their first ever meeting with Mr Kim.
It is not clear if they are embellishing the message’s significance, or who the private message is addressed to.
The US state department said on Tuesday it is in touch with the White House about a proposed meeting with the South Korean envoys, Reuters reported.
It appears both Koreas are trying to capitalise on eased tensions after the 2018 Pyeongchang Winter Olympics, which saw them march together under one flag. (Courtesy BBC)