"If an inter-Korean summit takes place, a related message could be delivered" to the North's leader, the presidential official told reporters, when asked to comment on the CNN report. The official did not elaborate on the content of the message.

CNN has cited a source saying that Trump's message includes "things that matter to the current course of action, things that have to lead to something positive for the US-DPRK summit."

"I believe (Kim) will be very, very curious about what my President (Moon) will have to say after his meeting with the Trump administration," the apparent South Korean source said. "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 nuclear negotiations have been in a stalemate after February's summit between Trump and Kim ended without an agreement due to differences over how to reconcile Washington's demands for denuclearization measures and Pyongyang's demand for sanctions relief.

The North's Kim said in a key policy speech earlier this month that he is willing to hold a third summit with Trump if the United States comes up with a new proposal that's acceptable to Pyongyang by the end of the year.

Since the speech, the North has been stepping up criticism of the US, with senior diplomats blasting US Secretary of State Mike Pompeo and National Security Adviser John Bolton by name for failing to understand Pyongyang's negotiating position and making irrelevant remarks.

The North also conducted a test-firing of a newly developed weapon last week. (Yonhap)