It’s going [to] be a very important meeting, the denuclearisation of the Korean peninsula,” he said.
Meanwhile, new Secretary of State Mike Pompeo said he had had a “good conversation” with North Korea’s leader Kim Jong-un in Pyongyang recently.
On Friday, Mr Kim and the South Korean President Moon Jae-in agreed to work to rid the peninsula of nuclear weapons.
The inter-Korean summit at the border came just months after warlike rhetoric from the North.
Mr Kim became the first North Korean leader to set foot in South Korea since the end of the Korean War in 1953.
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, MrPompeo told ABC News that Mr Kim was “prepared to… lay out a map that would help us achieve” denuclearisation.
MrPompeo 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.