Trump was aboard Air Force One, en route to the United States, when the call was made, according to Cheong Wa Dae.

Trump said the North Korean leader proved to be a "great" dialogue partner, also noting that their meeting has achieved more than any negotiations between working-level officials ever could.

Noting that the North has agreed to dismantle its missile engine test facility, the US president said the decision again demonstrated Kim's willingness to make changes, Cheong Wa Dae said in a press release.

The Trump-Kim summit ended with a joint statement signed by the two leaders in which the North agreed to work to recover the remains of US prisoners from the Korean War or those killed in action during the 1950-53 war.

Moon offered to begin discussions with North Korea for a joint excavation program between the three countries, noting the divided Koreas have already agreed to launch a similar program to find their own missing persons.

The two Koreas are currently scheduled to hold high-level military talks on Thursday.

Moon and Trump agreed to closely work together to implement the US-North Korea agreement.

"The two leaders noted the importance of thoroughly and swiftly implementing what has been agreed between the North and the US in the Singapore summit, and agreed to more closely consult and cooperate with each other to this end," Cheong Wa Dae said. (Yonhap)