(CNN) - South Korean President Moon Jae-in has a message from President Donald Trump to relay to North Korean leader Kim Jong Un, South Korean diplomatic sources told CNN Friday.
The message includes "things that matter to the current course of action, things that have to lead to something positive for the U.S.-DPRK summit," a source said. "I believe he (Kim) would be very, very curious about what my President (Moon) would have to say after his meeting with the Trump administration."
"President Moon has been clear and simple. Small deal, big deal, good or bad, something has to happen, the process has to be sustainable," the source continued.
CNN has reached out to the White House for comment.
Trump and Moon met at the White House a week ago to discuss plans for reviving the diplomatic process between the U.S. and North Korea.
At the meeting, South Korea and the U.S. "identified we are on the same page and on what needs to be done," noting that "the utility of the top-down approach is still there," adding that "there is no daylight between the U.S. and South Korea," a source said.
The Blue House believes that South Korea is "the architect" of the diplomatic process, a source said, and it is trying to reignite the momentum of dialogue toward another North Korea-South Korea summit which would could then lead to a third U.S.-North Korea summit.
South Korea believes Kim still wants to negotiate and that his mindset is that this is a critical juncture and that "unless substantive things happen by the end of this year, the momentum will die out," a source said.
On Wednesday, North Korea claimed a "new tactical guided weapons firing test," which was directed by Kim. Of the test, the source said, "I think he's taking care of his domestic audience. Some sources may have suggested you have to do something to soothe people in North Korea and Pyongyang. If he really wanted to do a formidable, important, heavy message to the U.S. or South Korea, he would not have done a minimal test."
The test came as denuclearization talks between the U.S. and North Korea have stalled following a failed second summit earlier this year in Vietnam between Kim and Trump. In February, Trump cut the summit short, and the two leaders left without a deal.
Recently, Kim and Trump have signaled that they're open to another meeting, but Kim called for the US to stop "its current way of calculation" in its approach to diplomatic talks.
North Korea's Foreign Ministry added to that on Thursday, saying if the U.S. wishes to continue talks, it should replace U.S. Secretary of State Mike Pompeo with someone "who is more careful and mature in communicating with us."
CNN's Veronica Stracqualursi and Betsy Klein contributed to this report.
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