Ri Yong-ho told the world body's annual General Assembly that continued sanctions were deepening its mistrust of the United States.
Known for its loyalty and cleverness, the Pungsan breed - a hunting dog with thick, creamy white coat, pointy ears and hazel eyes - is one of the National Treasures of North Korea.
Trump met Kim in Singapore in June for the first-ever summit between the two countries that have never signed a peace treaty.
"Without any trust in the USA there will be no confidence in our national security and under such circumstances, there is no way we will unilaterally disarm ourselves first", Ri said.
"We're doing great with North Korea", he said.
Both Kim and Trump want a second summit.
By contrast, Trump in his remarks to the assembly on Tuesday, thanked Kim "for his courage and for the steps he has taken".
The North Korean foreign minister contrasted Pyongyang's relations with Washington with the rapid progress made in inter-Korean relations through three summits this year, most recently September 18-20.
Ri said it was a "pipe dream" that continued sanctions and United States objection to a declaration to formally end the Korean war would ever bring the North to its knees. On Wednesday, US Secretary of State Mike Pompeo met with Ri in NY and accepted the North Korean leader's invitation to visit Pyongyang, the State Department said.
He said the United States is instead maintaining sanctions to keep up the pressure on the regime.
"However, we do not see any corresponding response from the USA", he said.
This came after June's historic meeting between US President Donald Trump and Kim Jong-un in Singapore, when they agreed in broad terms to work towards the nuclear-free Korean peninsula. "And then we fell in love".
Pyongyang has also made clear that they are looking for a formal declaration to the end of the Korean War.
"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.
North Korea's foreign minister put much of the blame for the stalled momentum on US domestic politics.
The Security Council has unanimously boosted sanctions since 2006 in a bid to choke off funding for Pyongyang's nuclear and ballistic missile programs.
Mr Moon said that he had been "able to confirm Chairman Kim's firm commitment to complete denuclearisation" and that he had also expressed his wish to meet Mr Trump again soon.