Washington (CNN) The historic diplomatic encounter planned for three weeks from now between President Donald Trump and North Korean despot Kim Jong Un appeared in doubt on Tuesday as Trump questioned whether preparations could be completed in time.

"There's a very substantial chance that it won't work out," Trump said in the Oval Office, where he was sitting for critical talks with his South Korean counterpart. "That doesn't mean that it won't work out over a period of time, but it may not work out for June 12."

It was the clearest indication to date that the audacious summit Trump agreed to in March may be at risk. Last week, North Korea adopted a harsh new tone and threatened to withdraw from the meeting, which is due to occur in Singapore.

Hours after Trump spoke, his Secretary of State Mike Pompeo sought to cast a more optimistic view of the talks, appearing for the first time in the State Department briefing room to insist a June 12 meet was still the goal.

"We're working to make sure that there is a common understanding about the contents of what will be discussed. But I'm optimistic," Pompeo said. "It could be something that comes right to the end and doesn't happen. As the President said, we'll see. And that is the place that we find ourselves."

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