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US President Donald Trump has said there is a "very substantial chance" a historic summit with North Korea's Kim Jong-un next month may not happen.

He said the North must meet conditions for the summit to go ahead though if it did not, it might happen "later", BBC reports.

Mr Trump was speaking as he received South Korea's President Moon Jae-in at the White House.

The North has said it may cancel the summit if the US insists on it giving up nuclear weapons unilaterally.

Mr Trump did not say what conditions the US had set for the summit but, asked by a reporter about the North's arsenal, he said "denuclearisation must take place".

The 12 June summit is due to take place in Singapore. It follows a historic meeting between the two Korean leaders in April.

Donald Trump told reporters: "We'll see what happens.

"There are certain conditions that we want and I think we'll get those conditions and if we don't we don't have the meeting.

"You go into deals that are 100% certain - it doesn't happen. You go into deals that have no chance and it happens and, sometimes, happens easily."

He also said Kim Jong-un's attitude had changed after his second visit to China, earlier this month.

Later in the day, during a news conference, Secretary of State Mike Pompeo adopted a more positive position, saying the US was still working towards the 12 June date.