Mr Trump has said his outreach to Mr Kim and their first meeting last June in Singapore opened a path to peace. But there is not yet a concrete plan for how denuclearisation could be implemented.
"As part of a bold new diplomacy, we continue our historic push for peace on the Korean Peninsula," Mr Trump said in his State of the Union address.
"If I had not been elected president of the United States, we would right now, in my opinion, be in a major war with North Korea."
Director of National Intelligence Dan Coats told Congress last week that US intelligence officials do not believe Mr Kim will eliminate his nuclear weapons or the capacity to build more because he believes they are key to the survival of the regime.
Last year, North Korea released American detainees, suspended nuclear and long-range missile tests and dismantled a nuclear test site and parts of a rocket launch facility without the presence of outside experts.
It has repeatedly demanded that the US reciprocate with measures including sanctions relief, but Washington has called for North Korea to take steps such as providing a detailed account of its nuclear and missile facilities that would be inspected and dismantled under a potential deal.
"Our hostages have come home, nuclear testing has stopped, and there has not been a missile launch in 15 months," Mr Trump said.
"Much work remains to be done, but my relationship with Kim Jong Un is a good one," he said in announcing their second meeting on February 27 and 28.
During the two-day summit, some experts say North Korea is likely to seek to trade the destruction of its main Yongbyon nuclear complex for a US promise to formally declare the end of the 1950-53 Korean War, open a liaison office in Pyongyang and allow the North to resume some lucrative economic projects with South Korea.
The Vietnamese city where the two leaders will meet was not announced.