The second summit is being planned for near the end of February, after Trump met with a senior North Korean official at the White House Friday.
"We had a very good meeting yesterday with North Korea. That was an incredible meeting," the US president told reporters at the White House.
"It lasted almost two hours and we've agreed to meet sometime probably the end of February. We've picked the country but we'll be announcing it in the future," he said.
Kim Yong-chol, known as a close aide to the North Korean leader, arrived in the US capital Thursday to try to finalize the details of the second summit.
The first summit in Singapore in June produced an agreement to work toward complete denuclearization of the Korean Peninsula in exchange for security guarantees for the North.
Negotiations to implement the deal have appeared to hit an impasse as the North demands sanctions relief and other US concessions for the steps it takes to dismantle its nuclear weapons program.
White House press secretary Sarah Sanders said Friday that sanctions on the country will remain "until we see fully and verified denuclearization."
Vietnam has been widely reported as the likely site for the next summit. Both the US and North Korea have embassies there.
"Kim Jong-un is looking very forward to it and so am I," Trump said. "We've made a lot of progress that has not been reported by the media. But we have made a lot of progress as far as denuclearization is concerned and we're talking about a lot of different things," he said. (Yonhap)