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DONALD Trump met with Kim Jong-un for their second historic summit in Vietnam.

But when exactly is being discussed this week and have the two leaders reached an agreement? Here's the latest.

 Trump and Kim Jong Un take a walk after their first meeting at the Vietnam summit
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Trump and Kim Jong Un take a walk after their first meeting at the Vietnam summitCredit: AP:Associated Press

What are Donald Trump and Kim Jong-un discussing at the Vietnam summit?

Trump reasserted his hopes for complete denuclearisation ahead of the summit.

Kim was expected to ask for relief from crushing US sanctions.

While the first meeting was all about breaking the ice after decades of war and bitter animosity between their countries, this time there will be pressure to agree to moves towards denuclearisation.

The leaders had dived into the second day of crunch talks to hammer out a deal of ridding North Korea of its deadly nuclear arsenal - but the planned signing ceremony was scrapped as the discussion ended without an accord.

At a press conference, the US President said the North Korean despot wanted the sanctions imposed on his crackpot regime lifted.

While insisting the two leaders had spent some "productive time" together, Trump said: "Sometimes you have to walk."

The US President continued: "They wanted the sanctions lifted. And we were unwilling to do that.

"We will end being very good friends with chairman Kim and North Korea. They have amazing potential.

"He has a certain vision it’s not exactly our vision. But it’s a lot closer than we were a year ago."

The brash New Yorker said that the North Korea leader wants to "denuke a portion" of his country - which was another point of contention for the US administration.

 Kim Jong Un and Donald Trump speak at the extended bilateral meeting
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Kim Jong Un and Donald Trump speak at the extended bilateral meetingCredit: AFP or licensors

Have they reached an agreement?

US Secretary of State Mike Pompeo also spoke about the failed summit, saying: "We made real progress. We didn’t get all the way.

"We didn’t agree something which would make sense for the United States of America."

Earlier, White House press secretary Sarah Sanders says the two leaders discussed denuclearization of the Korean Peninsula.

She adds: "No agreement was reached at this time, but their respective teams look forward to meeting in the future."

Still, Sanders is describing the meetings between Trump and Kim as "very good and constructive."

Trump and Kim departed the hotel where they've been holding summit negotiations far earlier than planned Thursday.

A joint agreement signing ceremony was scrapped.

It comes after President Trump insisted there was "no rush" on forging a lasting agreement - adding: "We just want to do the right deal".

They were joined by US Secretary of State Mike Pompeo and North Korean official Kim Yong Chol.

The chumminess between Chairman Kim and Trump marks a stark contrast to a year ago - when the US President threatened to rain "fire and fury" in Pyongyang over its nuke tests.

North Korea leader Kim Jong-un says he is ready to denuclearise during talks with US President Donald Trump
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