Speaking at a rally in Washington, Michigan, he said: "I think we will have a meeting over the next three or four weeks."
He said he hoped for successful negotiations on the denuclearisation of the Korean peninsula.
But the president added that he was ready to walk away if the talks did not work out.
North Korea has not publicly commented on Mr Trump's latest statements.
Earlier on Saturday, Mr Trump tweeted that "things are going well" and that preparations were being made for his summit with Mr Kim.
Separately, Mr Pompeo told ABC News that Mr Kim was "prepared to... lay out a map that would help us achieve" denuclearisation.
Mr Pompeo described the North Korean leader as "very well prepared" during their talks in Pyongyang.
US officials are still deciding where to hold the talks between President Trump and Mr Kim - but Mongolia and Singapore are understood to be two countries on the shortlist.
Mr Kim and Mr Moon said they would pursue talks with the US and China to formally end the Korean War, which ended in 1953 with a truce, not total peace.
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