During the West Virginia rally, Mr Trump told supporters that Mr Kim is interested in a second meeting.
However, earlier this month South Korean leader Moon Jae-in completed a high-profile, three-day visit to Pyongyang - the first by a Southern leader to the North's capital in a decade.
Washington is wary of agreeing to the declaration without Pyongyang first making significant disarmament moves.
"And then we fell in love, okay?"
He warned that if both countries continue to harbor mistrust, the summit's joint statement would suffer the same "fate of failure as all the previous agreements between the two countries".
Despite this, negotiations between the U.S. and North Korea have stalled since the Singapore summit.
U.S. Secretary of State Mike Pompeo met with Ri in NY and is planning to go to Pyongyang next month to continue discussions.
'He wrote me attractive letters.
"I was really being tough - and so was he".
Ri said it was a "pipe dream" that continued sanctions and USA objection to a declaration to formally end the Korean war would ever bring the North to its knees.
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The SEC lawsuit caused Tesla's stock to dip by as much as 11% in after-hours trading. This purchase price reflected a premium over Tesla's stock share price at the time.
Mr Trump was likely referring to the letters he received from Mr Kim that his White House spokeswoman Sarah Sanders described at the time as "a very warm, very positive letter."
The subject of North Korea-U.S. relations have been raised several times during the course of the week at the United Nations by a number of member states. How disgusting is that?
Trump took a much more optimistic view in his rally speech. "It's so easy to be presidential".
Kim had earlier compared comments by Trump to the bark of a "rabid dog", and Trump derided Kim as a "sick puppy" - before the apparent outbreak of puppy love.
Mr. Trump again called Ms. Warren "Pocahontas", reprising his nickname based on her previous unsubstantiated claims of Native American heritage, and said the Democratic Party has grown so liberal it's even outflanked the famously left-wing crusader.
China and Russian Federation argued that the UN Security Council should reward Pyongyang for steps taken.
Three senior US officials involved in North Korea policy said this week that no progress has been made in moving toward serious negotiations on eliminating or even halting Kim's nuclear weapons and ballistic missile programs.
Chairing a meeting of the UN Security Council just days earlier, Pompeo urged the global community to fully implement all sanctions on the North.
The Security Council has unanimously boosted sanctions since 2006 in a bid to choke off funding for Pyongyang's nuclear and ballistic missile programs.