Mr Trump said at the Saturday night rally in West Virginia: “He wrote me beautiful letters and they're great letters. We fell in love.”
He joked about criticism he would get from the news media for making a comment some would consider “unpresidential” and for being so positive about the North Korean leader.
“Why has President Trump given up so much?” President Trump said in his mock “news anchor” voice. “I didn't give up anything.”
But denuclearisation negotiations have stalled.
More than three months after the June summit in Singapore, North Korea's top diplomat Ri Yong Ho told world leaders at the UN General Assembly on Saturday that the North doesn't see a “corresponding response” from the US to North Korea's early disarmament moves.
Instead, he noted, the US is continuing sanctions aimed at keeping up pressure.
Mr Trump took a much more optimistic view in his rally speech.
“We're doing great with North Korea,” he said. “We were going to war with North Korea. Millions of people would have been killed. Now we have this great relationship.”
He said his efforts to improve relations with Mr Kim have brought positive results - ending rocket tests, helping free hostages and getting the remains of American servicemen returned home.
And he defended his unusual approach in talking about relations with Mr Kim.
“It's so easy to be presidential, but instead of having 10,000 people outside trying to get into this packed arena, we'd have about 200 people standing right there,” Mr Trump said, pointing at the crowd directly in front of him.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies