North Korea's foreign minister, Ri Yong Ho, told the UN General Assembly (UNGA) on Saturday that the country will in no way unilaterally disarm and that the US must first and foremost build trust with North Korea.
Trump began by talking of the massive threat that North Korea posed before he took office in January 2017.
But denuclearisation negotiations have stalled.
He noted that Kim is interested in a second meeting after their initial meeting in Singapore in June was hailed by Trump as a big step toward denuclearization of North Korea.
He said the continued sanctions are "deepening our mistrust" and deadlocking the current diplomacy.
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".
By contrast, Trump in his remarks to the assembly on Tuesday, thanked Kim "for his courage and for the steps he has taken".
Ri says it's a "pipe dream" that continued sanctions and U.S. objection to a declaration ending the Korean War will ever bring the North to its knees.
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U.S. President Donald Trump took his enthusiasm for his detente with North Korean leader Kim Jong Un to new heights on Saturday, declaring at a rally with supporters that "we fell in love" after exchanging letters. "And we would go back and forth", Trump said at a rally in West Virginia.
"Now they will say, 'Donald Trump said they fell in love".
He said the USA is instead maintaining sanctions to keep up the pressure on the regime.
The diplomat's comments come as Secretary of State Mike Pompeo seems to be on the verge of restarting deadlocked nuclear diplomacy more than three months after the summit.
On Saturday, September 29, the US President fuelled his "bromance" with Kim as he claimed that "they fell in love" after receiving "beautiful letters" from the leader of the nuclear-armed state.
The Security Council has unanimously boosted sanctions since 2006 in a bid to choke off funding for Pyongyang's nuclear and ballistic missile programs.
The Trump administration has been trying to revive nuclear talks with Kim Jong Un, the North's leader.