Donald Trump has become the first sitting US president to step into North Korea as he met the north's leader, Kim Jong-un, in the Korean demilitarised zone (DMZ).

Key points: Donald Trump has become the first sitting US President to enter North Korea

Donald Trump has become the first sitting US President to enter North Korea South Korean leader Moon Jae-in has described the President's decision to meet Kim Jong-un as "brave"

South Korean leader Moon Jae-in has described the President's decision to meet Kim Jong-un as "brave" Mr Trump became the first sitting US president to meet with the leader of North Korea last year

The meeting marked the first time the leaders of the US and North Korea have met on the front line of the Korean peninsula conflict.

They shook hands over the border before Mr Kim invited Mr Trump to step across, echoing his invitation to South Korea's President Moon Jae-in during their historic meeting in April, 2018.

The two leaders walked a little way into the North, shook hands again in front of North Korean press, and walked back into the South for their sit-down discussion.

Donald Trump steps from the DMZ into North Korea at Kim Jong-un's invitation. ( ABC News )

It was Mr Trump and Mr Kim's third meeting and Mr Trump confirmed he extended an invitation for Mr Kim to meet him in the US, although he gave no indication of any reaction to that request.

"I said 'at the right time you will come over' [but] we have a ways to go yet, so we will see," Mr Trump said.

"Anytime he wants to do it. Let's see what happens.

Ahead of the meeting, Mr Trump said a handshake "means a lot". ( Reuters: Kevin Lamarque )

"No hurry, no real speed," he added.

Both leaders have previously committed to the "complete denuclearisation" of the Korean peninsula, but their second meeting earlier this year ended in no deal.

The meeting comes after Mr Trump declared his desire to meet Mr Kim at the border "just to shake his hand and say Hello(?)!" on Saturday.

Mr Trump said sanctions on North Korea would remain in place for now. ( AP: Susan Walsh )

The South Korean President, who announced that Mr Kim accepted Mr Trump's invitation to meet, praised the two leaders for "being so brave" to hold the meeting ahead of the event.

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"I hope President Trump will go down in history as the president who achieves peace on Korean Peninsula," Mr Moon said.

Mr Trump said he looked forward to meeting with Mr Kim, but sought to dampen expectations, predicting it would be "very short".

"Virtually a handshake, but that's OK. A handshake means a lot," he said.

After the meeting, Mr Trump and Mr Moon farewelled Mr Kim before heading back inside for another media briefing, during which the US leader described it as a "very legendary day" that was "great for the world".

Moon Jae-in, right, described Donald Trump as "brave" for meeting the North Korean leader. ( Reuters )

"It will be even more historic if something comes out of it," he said.

"You see what is going on and you see what is happening and the level of relationship as opposed to the way it was when I came into office. When I came into office, it was a fiery mess, bad things were going on.

Donald Trump and Kim Jong-un performed a historic handshake on both sides of the border. ( Reuters: Kevin Lamarque )

"For two-and-a-half years we have had peace, with nothing signed, just based on relationships."

"Very big stuff. Pretty complicated. But not as complicated as people think," he added.

Mr Trump was light on specifics, but said the US and the North had "agreed to have teams set up", with the American team led by Secretary of State Mike Pompeo, which Mr Moon said was to further negotiations "in the near future".

Officials spent Sunday morning working out logistical and security details, Mr Trump said during a media appearance with Mr Moon.

Presidential visits to the DMZ are traditionally carefully guarded secrets for security reasons.

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'The flower of peace is truly blossoming'

Ahead of the meeting, Mr Trump said at a news conference in Japan that he would "feel very comfortable" crossing the border into North Korea if Mr Kim showed up, saying he would "have no problem" becoming the first sitting US president to do so.

It was not immediately clear what the agenda, if any, would be for the potential third Trump-Kim meeting.

North Korea's first Vice Foreign Minister, Choe Son-hui, said the meeting would serve as "another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations".

Meeting with Mr Trump at South Korea's presidential Blue House on Sunday before the pair flew to the DMZ, Mr Moon said when he saw Mr Trump's invitation to Mr Kim, "I could really feel that the flower of peace was truly blossoming on the Korean Peninsula".

Mr Moon added that the meeting would be a "significant milestone in the peace process".

Even Pope Francis praised the meeting and said he hoped it would lead to peace.

"In the last few hours we saw in Korea a good example of the culture of encounter," he said at his weekly address in St Peter's Square.

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"I salute the protagonists, with a prayer that such a significant gesture will be a further step on the road to peace, not only on that peninsula, but for the good of the entire world."

Mr Trump's summit with Mr Kim in Vietnam earlier this year collapsed without an agreement for denuclearising the Korean Peninsula.

He became the first sitting US president to meet with the leader of the isolated nation last year, when they signed an agreement in Singapore to bring the North toward denuclearisation.

Substantive talks between the nations have largely broken down since then.

The North has baulked at Mr Trump's insistence that it give up its weapons before it sees relief from crushing international sanctions, which Mr Trump confirmed would remain in place for now.

Still, Mr Trump has sought to praise Mr Kim — in hopes of keeping the prospects of a deal alive — and the two have traded letters in recent weeks.

Every US president since Ronald Reagan has visited the 1953 armistice line, except for George HW Bush, who visited when he was vice-president.

ABC with wires