Key points:

Kim Jong-un commits to denuclearisation in a joint document with Donald Trump.

Trump calls Kim "a very talented man", may invite him to the White House.

Kim's team had problems with the pen provided at the signing ceremony.

North Korean leader Kim Jong-un has committed to "complete denuclearisation of the Korean Peninsula" in a joint text.

Kim and US President Donald Trump signed the "historic" document after their Singapore meeting on Tuesday.

READ MORE Full text of the Trump-Kim summit agreement

"It's pretty comprehensive," Trump said about the document, adding that denuclearisation could begin "very quickly".

The statement said "President Trump committed to provide security guarantees to the DPRK, and Chairman Kim Jong-un reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula".

It said "President Trump and Chairman Kim Jong-un state the following:"

1. The United States and the DPRK commit to establish new U.S.-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity.

2. The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula.

3. Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work towards complete denuclearisation of the Korean Peninsula.

4. The United States and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified.

The text made no mention of US demands for "complete, verifiable and irreversible denuclearisation" - jargon for scrapping weapons and committing to inspections - but did restate a vaguer commitment.

ZOOM IN ON THE TEXT: "President Trump committed to provide security guarantees to the DPRK, and Chairman Kim Jong Un reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula." pic.twitter.com/vXBeIMP81i — Conor Finnegan (@cjf39) June 12, 2018

Speaking about Kim, Trump said "we have developed a very special bond" and is "absolutely" willing to invite Kim to the White House.

"We'll meet again ... We will meet many times."

He also said Kim was "a very talented man and he loves his country very much".

Via a translator, Kim said "today, we had a historic meeting and decided to leave the past behind ... The world will see a major change."

The carefully-choreographed signing went slightly off script when it appeared Kim's team did not want him to use the provided pen. A member of Kim's team swooped in at the last minute and swapped the venue's pen with one of their own.

Earlier, Trump hailed his summit with Kim Jong-un in Singapore as a "fantastic" sit-down.

"We had a really fantastic meeting," Trump said as he strolled out of the Capella Hotel side-by-side with the North Korean leader after their working lunch on Tuesday.

"A lot of progress. Really, very positive, I think better than anybody could have expected, top of the line, really good," Trump added, before showing Kim the interior of "The Beast", his armour-plated limousine.

AAP

Historic handshake

Trump and Kim shared warm words and a historic handshake on Tuesday as they held an unprecedented summit to confront a decades-old nuclear stand-off and enmity stretching back to the Cold War.