At the UN, North Korea repeated its request to the USA to declare the end of the 1950-1953 Korean war, which ended with a ceasefire but without a peace treaty.
Pompeo is planning to visit Pyongyang next month to prepare for a second Kim-Trump summit.
Kim expressed an openness to denuclearizing during a summit with South Korean President Moon Jae In last week, but indicated North Korea would only do so if the US took undefined "corresponding measures".
This was decidedly so during an exchange of threats between Washington and Pyongyang that accompanied a run of increasingly powerful weapons tests past year that put the North on the brink of its claim to be a full-fledged nuclear power, and had some fearing war.
North Korea's foreign minister said Saturday that his government would not denuclearize before it has sufficient trust in the United States.
"And then we fell in love, okay?"
"We are well into a diplomatic process, and we hope - indeed, we want - to see this through to a successful end", Pompeo said this past week.
"That was a big, big problem", he told his supporters.
China says can't hold US trade talks with 'knife to the throat'
The new USA duties covers thousands of Chinese-made products, including electronics, food, tools and housewares. This is the case in other developed countries and is allowed under World Trade Organization rules, he said.
Trump in recent days has said his warm relationship with Kim gives him confidence that the two sides will make progress toward denuclearization, bragging that the North Korean strongman had recently written him "two of the most handsome letters".
Mr Trump joked about the criticism he would receive following his positive comments about the North Korean dictator, saying some would consider it "unpresidential".
Despite the warmer tone to the relationship, North Korea has not complied with U.S. demands to provide a complete inventory of its weapons programs and take irreversible steps to give up its arsenal.
"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", the foreign minister said Saturday.
"Why has President Trump given up so much?" We went back and forth, then we fell in love, ' he said.
"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", Trump said, pointing at the crowd directly in front of him.
In June, Mr Trump met with the North Korean leader in Singapore as part of an attempt to push his regime into denuclearisation.