President Trump met Mr Kim in Vietnam on Wednesday and the pair were pictured exchanging a warm handshake during their second summit.
Addressing Mr Kim during a scheduled media appearance, Mr Trump spoke about North Korea’s economy, saying: ‘Your country has tremendous economic potential. Unbelievable. Unlimited.’
He added: ‘I think you will have a tremendous future with your country and great leader. And I look forward to watching it happen and helping it happen. And we will help it happen.’
The two leaders exchanged handshakes, laughs and small talk at the Sofitel Legend Metropole Hanoi, where they were scheduled to meet for 20 minutes before sitting down for what the White House has described as a “social dinner”.
Mr Trump told reporters of the meeting: “We look forward to it, we both do.”
Asked whether he might formally end the Korean War, he responded: “We’ll see.”
Mr Trump has made the case that North Korea could thrive economically like Vietnam if the North ends its pursuit of nuclear weapons.
Mr Trump said: “We’ll see what happens, but he wants to do something great.”
Before the summit, President Trump had told how he hoped for “great things” from his second meeting with North Korea’s leader as he paid a courtesy call on his Vietnamese hosts.
Mr Kim was expected to take in some sights before the leaders open their second nuclear summit with private talks and a social dinner.
Mr Trump and Mr Kim first met last June in Singapore, a summit that was long on historic pageantry but short on any enforceable agreements for North Korea to give up its nuclear arsenal.
North Korea has spent decades, at great economic sacrifice, building its nuclear program, and there is widespread scepticism that it will give away that program without getting something substantial from the US. That could be a declaration to end the Korean War.
While Mr Trump wants Mr Kim to agree to dismantle his nuclear sites in a verifiable way, Mr Kim is seeking relief from crushing US sanctions hobbling his economy.
Other items being discussed are opening liaison offices in both North Korea and the United States.
North and South Korea also want sanctions dialled back so they can resurrect two major symbols of rapprochement that provided much-needed hard currency to North Korea: a jointly run factory park in Kaesong and South Korean tours to the North’s scenic Diamond Mountain resort.