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".

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.

Meanwhile, North Korea has agreed to let in journalists from the South to watch the dismantling of its nuclear test site. The group, who had earlier been denied visas, will join a team of international media who are in the country to visit Punggye-ri over the next few days.

The demolition of the site has been billed as a goodwill gesture but may be delayed by bad weather.

Mr 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.

He commended China for offering "historic assistance" in putting pressure on North Korea.

Analysis by the BBC's Barbara Plett Usher in Washington

The optimistic build-up to the summit gave way to a reality check that was bound to happen sooner or later.

With Kim Jong-un tapping the brakes and refusing to accept "unilateral demands" to disarm, President Trump also took a step back. He set his own conditions, although he didn't say what they were.

He did stress that it would be worth it for the North Korean leader to risk denuclearisation, throwing the ball back into Mr Kim's court.

The build-up to the summit has been shaped by an unusual degree of public showmanship by both leaders, a diplomatic version of their hostile exchanges last year. But while the threats and insults worked at the rhetorical level, this is about substantive issues where the detail matters.

President Moon Jae-in also has his spin. He really wants to seize this opportunity for South Korea's sake and continues to be determined in his optimism, leaving some here wondering whether he's been overstating Kim Jong-un's willingness to deal.

North Korea cancelled high-level talks with South Korea, saying the South's joint military exercises with the US - which it had previously said it would tolerate - were a "provocation".

Pyongyang then accused US national security adviser John Bolton of making "reckless statements" for his suggestion that the North could follow a "Libya model" of denuclearisation.

That was a reference to Libya's former leader, Muammar Gaddafi, who agreed to give up nuclear weapons in 2003 and was later killed by Western-backed rebels.

Mr Trump later denied the US would follow the "Libyan model" if an agreement was reached with North Korea.

"That model would take place if we don't make a deal, most likely. But if we make a deal, I think Kim Jong-un is going to be very, very happy."

It would be historic as no sitting US president has ever met a North Korean leader.

Mr Trump accepted North Korea's invitation for direct talks after more than a year of heated rhetoric and with global concern that hostilities might escalate into military confrontation.

The New York Times reported on Sunday that Mr Trump was asking aides and advisers whether the meeting should go ahead.

North Korea conducted several nuclear tests over the past few years and developed long-distance missiles which, it says, can carry nuclear bombs as far as the US mainland.

Many observers had argued before Mr Trump met Mr Moon that there was too much at stake for Washington and Pyongyang not to proceed with the Singapore summit.

However, Pyongyang's professed commitment to "denuclearisation" is likely to differ from Washington's demand for "comprehensive, verifiable and irreversible" nuclear disarmament.

A group of Western, Russian and Chinese journalists have been invited by the North to its remote Punggye-ri nuclear test site ahead of its demolition.

They were flown into the North Korean port city of Wonsan but their onward journey was postponed by bad weather, Tom Cheshire from the UK's Sky News tweets.

The site, in the mountainous north-east, is thought to be the North's main nuclear facility and the only active nuclear testing site in the world.

Testing has taken place in a system of tunnels dug below nearby Mount Mantap.