Since Pyongyang condemned the leaflet launches — usually attached to hot air balloons or floated in bottles — the Unification ministry has filed a police complaint against two defector groups and warned of a “thorough crackdown” against activists.
On Monday, the left-leaning Moon urged the North not to “close the window of dialogue”.
The two Koreas remain technically at war after Korean War hostilities ended with an armistice in 1953 that was never replaced with a peace treaty.
Last week the North criticized Trump in a stinging denunciation of the US on the second anniversary of the Singapore summit, with its foreign minister Ri Son Gwon accusing Washington of seeking regime change.
US diplomats insist that they believe Kim promised in Singapore to give up his nuclear arsenal, something Pyongyang has taken no steps to do.
The North is under multiple international sanctions over its banned weapons programs.
It believes it deserves to be rewarded for its moratorium on nuclear and intercontinental ballistic missile tests and the disabling of its atomic test site, along with the return of jailed US citizens and remains of soldiers killed in the Korean War.
“Nothing is more hypocritical than an empty promise,” Ri said in his statement, carried by the official KCNA news agency.
Cheong Seong-chang, director of the Sejong Institute’s Center for North Korean Studies, said: “North Korea is frustrated that the South has failed to offer an alternative plan to revive the US-North talks, let alone create a right atmosphere for the revival.
“It has concluded the South has failed as a mediator in the process.”