US President Donald Trump and North Korean leader Kim Jong Un have made history with a handshake and greeting before a one-on-one meeting in Singapore.

The discussions will give both a chance to size each other up and start discussions that could open the door to negotiations on denuclearisation of the Korean Peninsula.

The two leaders exchanged a handshake, arm and back pats, and initial words at a secluded island resort off the coast of Singapore.

Trump had a distinct height advantage over Kim and directed the younger man in the manner of a host. Kim flashed a smile before the cameras. 

5:50pm 

Trump says he "absolutely" would invite Kim to the White House.

Kim declares "world will see a major change" and he and Trump "decided to leave the past behind" as they sign documents. 

5:45pm

Trump and Kim have signed what Trump says is a "very important" and "pretty comprehensive" document.

But Trump is refusing to tell reporters what the declaration says. The document is set to be handed out to reporters later.

Trump said Tuesday as the leaders wrapped up their historic summit in Singapore that he and Kim "have developed a very special bond" during their day together. 

And he says, "Both sides are going to be impressed with the result."

Trump also said the North Korea denuclearisation process would be starting "very quickly".

Kim told reporters that "the world will see a major change," though it's unclear how.

Kim said he and Trump "decided to leave the past behind" as they signed the document.

The summit marked the first between a sitting US president and a North Korean leader.

Trump says he "absolutely" would invite Kim to the White House.

5:40pm

Trump and Kim have signed an unspecified document in Singapore.

Trump calls it "pretty comprehensive" but details of what the document contained are still unknown.

Trump says the North Korea denuclearisation process will be starting "very quickly".

Trump said after the summit with Kim that: "We have developed a very special bond".

5pm

Trump has given Kim a rare peek inside the US presidential limousine.

As the two leaders strolled around the grounds of the Singapore resort where they're having their summit Tuesday, they walked up to the US limousine nicknamed The Beast.

Trump can be seen talking and gesturing before a Secret Service agent opens the door and the leaders look in.

It wasn't immediately clear how Kim felt about the presidential tour, but he seemed to be smiling.

4:55pm 

Trump says he and Kim will be signing a document shortly.

Trump declined to specify what exactly the leaders would be signing.

Trump said after emerging from hours of talks with Kim on Tuesday in Singapore that "we're going right now for a signing."

Asked what he'd be signing, Trump said: "We're going to be announcing that in a couple of minutes."

4:45pm

Trump says his summit with Kim went "better than anybody could imagine".

The leaders emerged from a working lunch and strolled together down a paved walkway Tuesday before stopping and posing before the waiting news media.

Trump said the meeting is "going great. We had a really fantastic meeting."

He added that there has been "a lot of progress. Really very positive. I think better than anybody could imagine."

The working lunch was the final official event scheduled for the leaders before they go their separate ways.

Trump is scheduled to address the press corps and then begin the journey back to Washington.

4:25pm

Trump joked about his appearance as he prepared to sit down to lunch with Kim.

Trump said to photographers at Tuesday's summit in Singapore: "Getting a good picture, everybody? So we look nice and handsome and thin? Perfect."

A video feed provided by the summit host showed Trump, Kim and their aides taking their places at a long table.

Salad courses were prepositioned on the table along with flower bouquets. 

Trump took his spot in the middle of the table, and Kim opposite him.

Trump was joined by Secretary of State Mike Pompeo, White House press secretary Sarah Huckabee Sanders and a few other aides.

The lunch menu includes beef short ribs, sweet and sour crispy pork, and braised codfish.

Independent journalists covering Trump's summit were not allowed in to witness the start of the lunch in Singapore.

3:45pm

South Korean President Moon Jae-in says he "hardly slept" in anticipation of the United States-North Korea summit in Singapore.

Moon and other officials watched the live broadcast of the summit before a South Korean Cabinet meeting in his presidential office Tuesday.

Moon smiled and nodded as he watched Trump and Kim meet.

Moon has met Kim twice in recent months and helped arrange the US-North Korean summit.

Moon said he "ardently aspires" for the success of the summit and hopes it brings complete denuclearization and peace to the Korean Peninsula. 

Fighting in the Korean War ended with an armistice in July 1953.

That armistice has yet to be replaced with a peace treaty, leaving the peninsula in a technical state of war.

3:35pm

Former NBA star Dennis Rodman says all the pressure is on Trump in the historic meeting with Kim.

Rodman told The Associated Press on Tuesday that it's up to Trump to prove he can be trusted by Kim and the North Korean people.

The basketball Hall of Famer says it will take multiple visits for the countries to have any hope of a peaceful relationship.

Rodman joked that he should be pushing for the Nobel Peace Prize, or "at least give me a piece of it."

He struck up an unlikely friendship with Kim over their shared love of basketball and has visited North Korea several times but had no official role in the summit. 

3:25pm

Donald Trump and Kim Jong Un are chatting over a lunch of beef short ribs, sweet and sour crispy pork, and braised codfish.

Details released by the White House show that lunch began Tuesday with a prawn cocktail and avocado salad, and green mango kerabu with honey lime dressing and octopus.

Side dishes included potato dauphinois, steamed broccolini, fried rice and Asian vegetables.

Dessert included dark chocolate tartlet and Haagen-Dazs vanilla ice cream.

Among those joining the leaders on the US side were Secretary of State Mike Pompeo, White House chief of staff John Kelly and national security adviser John Bolton.

The North Korean delegation included Kim Yong Chol, a top aide to Kim Jong Un who recently met Trump at the White House.

2:30pm

Former NBA star Dennis Rodman says he received a call from the White House ahead of Trump's historic meeting with Kim.

Rodman told CNN in an interview from Singapore on Tuesday that a White House staffer called the former Celebrity Apprentice contestant to tell him the president was proud of him.

The White House did not immediately respond to questions about the call.

Rodman struck up an unlikely friendship with Kim over their shared love of basketball, but he says former President Barack Obama never took him seriously.

Rodman described Kim as a "big kid" who wants to see the world and he expressed hope that the two leaders will make progress.

2:10pm

Trump is sounding optimistic about his ability to persuade North Korea to abandon its nuclear weapons programme after a lengthy one-on-one meeting with Kim.

Trump said Tuesday at the beginning of expanded discussions with aides from both countries that "We will solve a big problem" and "a big dilemma".

He talked about the pair achieving "tremendous success together" and predicts that "it will be successful. It will be done."

It was hard to hear the US president and Kim over the constant clicking of camera shutters, and it remains unclear precisely what he was referring to.

But Kim appeared to echo Trump's optimism.

1:55pm

Trump says that his one-on-one meeting with Kim was "very, very good" and that the two have an "excellent relationship."

Trump and Kim met for about 40 minutes Tuesday one-on-one, joined only by interpreters.

Trump made the comments as he and Kim walked together along balcony as they headed to a larger meeting with aides.

Trump was flanked in the larger meeting by chief of staff John Kelly, Secretary of State Mike Pompeo and national security adviser John Bolton.

They sat across the table from Kim and his team.

1:20pm

Trump is predicting that he and Kim will have "a terrific relationship" as they meet face to face for the first time.

Trump said Tuesday after meeting Kim that he's feeling "really great."

He says, "We're going to have a great discussion and a terrific relationship."

Kim says through an interpreter that it "was not easy to get here" and that there "were obstacles but we overcame them to be here."

The two men are expected to meet on their own for the better part of an hour, with only a pair of interpreters in the room.

That decision has raised concerns about the risk of holding such a monumental meeting with barely anyone to bear witness.

1:05pm

Trump and Kim are sharing a historic handshake as they meet for the first time.

The two clasped hands for a long while Tuesday as they posed for photos in front of a row of US and North Korean flags.

Trump then directed Kim to walk down a hallway, where they briefly spoke.

It's the first ever meeting between a sitting US president and North Korean leader.

Trump and Kim arrived not long ago on Singapore's Sentosa Island, the site of their unprecedented summit.

It's aimed at settling a standoff over Pyongyang's nuclear arsenal.

The two will huddle alone for roughly 45 minutes before being joined by aides for a larger meeting and working lunch.

Trump has said he'll know within minutes whether a deal can be made.

12:35pm

Kim has arrived at Singapore's Sentosa Island, where he'll be meeting shortly face-to-face with Trump.

The two men are expected to share a handshake before they meet alone with a pair of interpreters for roughly 45 minutes while their entourages wait nearby.

After the intimate huddle, they're scheduled to hold a larger meeting and working lunch.

Trump's chief of staff, national security adviser and secretary of state are among those expected to join.

The meeting is the first sit-down between a sitting US president and North Korean leader and is meant to settle a standoff over Pyongyang's nuclear program.

Trump earlier defended his decision to meet with Kim, tweeting that North Korea has already released three detainees and that missile tests have halted. 

12:20pm

Trump has arrived on Singapore's Sentosa Island for his historic meeting with Kim.

Trump's motorcade pulled into the grounds of the Capella Hotel at 8:13am, local time.

He is scheduled to meet Kim for the first time at 9am (1pm NZT).

Kim is also en route to Sentosa Island for the meeting to discuss the fate of his country's nuclear weapons arsenal.

11:50pm

North Korea's state media has reported on Kim's late-night tour of Singapore with unusual speed.

Pyongyang's official Rodong Sinmun on Tuesday filled its front page with photos of his visits to Singapore's landmarks, including the Flower Dome at Gardens by the Bay and the Marina Bay Sands resort.

The North's Korean Central News Agency quoted Kim as saying that Singapore is "clean and beautiful and every building is stylish" and that he will learn "a lot from the good knowledge and experience of Singapore in various fields in the future."

It's rare that security-obsessed North Korea reports on Kim's activities within hours.

When Kim visited China for meetings with Chinese President Xi Jinping in March and May, state media didn't report on the trips until after he returned home.

Some experts say North Korea is trying to keep up with the speed of the Western media in Singapore.

- AP