North and South Korea say they will jointly push for talks with the United State and also potentially China to officially end the 1950-53 Korean War, which stopped in an armistice and left the Koreas still technically at war.

North Korean leader Kim Jong Un and South Korean President Moon Jae-in announced after their summit on Friday that the Koreas will push for three-way talks including Washington or four-way talks that also include Beijing on converting the armistice into a peace treaty and establishing permanent peace on the Korean Peninsula.

The Koreas said they hope the parties will be able to declare an official end to the war by the end of this year.

While President Donald Trump has given his "blessing" for the Koreas to discuss an end to the war, there can be no real solution without the involvement of Washington and other parties that fought in the war because South Korea wasn't a direct signatory to the armistice that stopped the fighting

Meanwhile, the two Koreas also agreed to open a permanent communication office in the North Korean town of Kaesong and resume temporary reunions between relatives separated by the 1950-53 Korean War.

North Korean leader Kim and South Korean President Moon also said that the Koreas will seek to expand civilian exchanges and pursue joint sports and cultural events.

The family reunions are expected to take place around Aug. 15, an anniversary for both Koreas celebrating their peninsula's liberation from Japanese colonial rule after the end of World War II.

Moon will visit Pyongyang in "the fall", the two leaders said, also agreeing to hold "regular meetings and direct telephone conversations".

The so-called Panmunjom Declaration capped an extraordinary day unthinkable only months ago, as the nuclear-armed North carried out a series of missile launches and its sixth atomic blast.

Kim said he was "filled with emotion" after stepping over the concrete blocks into the South, making him the first North Korean leader to set foot there since the shooting stopped in the Korean War.

At Kim's impromptu invitation the two men briefly crossed hand-in-hand into the North before walking to the Peace House building on the southern side of the truce village of Panmunjom for the summit -- only the third of its kind since hostilities ceased in 1953.

"I came here determined to send a starting signal at the threshold of a new history," said Kim.

After the summit, he pledged that the two Koreas will ensure they did not "repeat the unfortunate history in which past inter-Korea agreements... fizzled out after beginning".

The two previous Korean summits in 2000 and 2007, both of them in Pyongyang, also ended with displays of affection and similar pledges, but the agreements ultimately came to naught.

With the North's atomic arsenal high on the agenda, South Korean President Moon Jae-in responded that the North's announced moratorium on nuclear testing and long-range missile launches was "very significant."

It was the highest-level encounter yet in a whirlwind of nuclear diplomacy, and intended to pave the way for a much-anticipated encounter between Kim and U.S. President Donald Trump.

Olympic ice-breaker

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

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

Moon seized on the South's Winter Olympics as an opportunity to broker dialogue between them, and has said his meeting with Kim will serve to set up the summit between Pyongyang and Washington.

The White House said it hoped the summit would "achieve progress toward a future of peace and prosperity for the entire Korean Peninsula".

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.

Seoul had played down expectations before the summit, saying the North's technological advances in its nuclear and missile program made the summit "all the more difficult".

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

When Kim visited the North's key backer Beijing last month in only his first foreign trip as leader, China's state media cited him as saying that the issue could be resolved, as long as Seoul and Washington take "progressive and synchronous measures for the realization of peace".

In the past, North Korean support for denuclearization of the "Korean peninsula" has been code for the removal of U.S. troops from the South and the end of its nuclear umbrella over its security ally -- prospects unthinkable in Washington.

Moon said he hoped they would have further meetings on both sides of the border, and Kim offered to visit Seoul "any time" he was invited.

After a morning session lasting an hour and 40 minutes, Kim crossed back to the North for lunch, a dozen security guards jogging alongside his limousine.

Before the afternoon session, Moon and Kim held a symbolic tree planting ceremony on the demarcation line.

The soil came from Mount Paektu, on the North's border with China, and Mount Halla, on the South's southern island of Jeju.

After signing the agreement the leaders and their wives attended a banquet before Kim was to return to the North.