The two leaders agreed to "resume and push forward productive dialogues for making a new breakthrough in the denuclearisation of the Korean peninsula", the official Korean Central News Agency said.

After a Twitter invitation by the US president on Saturday, the two men met a day later in the strip of land that has divided the peninsula for 66 years since the end of the Korean War, when their countries and their allies fought each other to a standstill.

Kim and Trump shook hands over the concrete blocks dividing North and South before Trump walked a few paces into Pyongyang's territory -- the first US president ever to set foot on North Korean soil.

"The top leaders of the DPRK and the US exchanging historic handshakes at Panmunjom" was an "amazing event", KCNA said, describing the truce village as a "place that had been known as the symbol of division".

The meeting took place "at the suggestion of Trump", it added.

The impromptu meeting in the DMZ was full of symbolism.

Trump's border-crossing -- which he said was uncertain until the last moment -- was an extraordinary sequel to the scene at Kim's first summit with Moon Jae-in last year, when the young leader invited the South Korean president to walk over the Military Demarcation Line, as the border is officially known.

"It was an honour that you asked me to step over that line, and I was proud to step over the line," Trump told Kim.

KCNA described it as a "historic moment", marking the "first time in history" a sitting US President set foot on North Korean soil.

Analysts have been divided on Sunday's events, some saying they spurred new momentum into deadlocked nuclear talks, while others described them as "reality show theatrics".

- 'Mysterious force' -

The first Trump-Kim summit took place in a blaze of publicity in Singapore last year but produced only a vaguely worded pledge about denuclearisation.

A second meeting in Vietnam in February collapsed after the pair failed to reach an agreement over sanctions relief and what the North was willing to give in return.

Contact between the two sides has since been minimal -- with Pyongyang issuing frequent criticisms of the US position -- but the two leaders exchanged a series of letters before Trump issued his offer to meet at the DMZ.

Trump said after Sunday's meeting that they had agreed working-level talks on the North's weapons programme would take place within weeks.

He also floated the idea of sanctions relief -- repeatedly demanded by Pyongyang -- and said he invited the North Korean leader to the White House.

Such a trip would have to come "at the right time", Trump added.

KCNA said Kim and Trump discussed "issues of mutual concern and interest which become a stumbling block in solving those issues".

The two leaders "agreed to keep in close touch in the future", it added.

KCNA cited Kim lauding their "good personal relations," saying they would "produce good results unpredictable by others and work as a mysterious force overcoming manifold difficulties and obstacles in the future, too".

It also said Kim had exchanged "warm greetings" with South Korean President Moon Jae-in, who met the two men as they returned to his side of the border.

KCNA accorded Moon his formal title despite Pyongyang denouncing the South's authorities only last week, saying they "have nothing to meddle in the dialogue".