Things 'going very well,' Trump says after talk with South Korea's Moon Jae-in

US President Donald Trump said Saturday that "things are going very well" after talking with South Korea's President Moon Jae-in about an upcoming summit with North Korean leader Kim Jong Un.

"Just had a long and very good talk with President Moon of South Korea. Things are going very well, time and location of meeting with North Korea is being set," Trump wrote on Twitter.

"Also spoke to Prime Minister (Shinzo) Abe of Japan to inform him of the ongoing negotiations," he wrote.

Moon met with Kim in a historic summit, agreeing on Friday to pursue a permanent peace and the complete denuclearization of the Korean peninsula.

An armistice brought the fighting on the Korean peninsula to an end in 1953, but 65 years later, a final peace agreement has still not been reached.

The Moon-Kim meeting has raised expectations for Trump's own planned summit with the North Korean leader, the date and location of which have not yet been finalized.

Mongolia and Singapore are the final two sites under consideration for the summit, CBS News reported, though Singapore's Prime Minister Lee Hsien Loong said Saturday that there had been no formal request for his city-state to host the meeting.

Last year, Pyongyang carried out its sixth nuclear test, by far its most powerful to date, and launched missiles capable of reaching the US mainland.

Its actions sent tensions soaring as Kim and Trump traded personal insults and threats of war.

Trump has demanded the North give up its weapons, and Washington is pressing for it to do so in a complete, verifiable and irreversible way.

Pyongyang is demanding as yet unspecified security guarantees to discuss its arsenal.