He said Secretary of State Mike Pompeo had very good talks with Kim over the weekend and that three or four locations were being considered.
Pompeo echoed Trump's comments when he spoke briefly to reporters during a Tuesdayafternoon visit to the White House.
"While there's still a long way to go and much work to do, we can now see a path where we will achieve (our) ultimate goal, which is the full and final verified denuclearization of North Korea," he said.
Trump and Kim held a historic first summit in Singapore on June 12 at which Kim pledged to work toward denuclearization of the Korean peninsula. His actions have fallen short, however, of Washington's demands for a complete inventory of its weapons and facilities and irreversible steps to give up its nuclear arsenal, which could threaten the United States.
'NO ROCKETS FLYING'
Still, Trump was upbeat on progress so far.
"You got no rockets flying, you have no missiles flying, you have no nuclear testing," Trump said in the Oval Office. "We've made incredible progress - beyond incredible.
"But I have agreed to meet," he said. "We have a very good relationship with Chairman Kim. I like him, he likes me, the relationship is good."
Pompeo said on Monday the two sides were "pretty close" to agreeing on details for a secondsummit.
He added that Kim had said he was ready to allow international inspectors into North Korea'sPunggye-ri nuclear testing site and the Sohae missile engine test facility as soon as the United States and North Korea agreed on logistics.
But experts questioned what Pompeo achieved on Sunday on his fourth visit to Pyongyang this year. They said the North Korean leader appeared simply to be repackaging and dragging out past pledges.
Trump noted that the United States had not lifted the "very big sanctions" it has imposed on Pyongyang.
"I'd love to remove them, but we have to get something for doing it," Trump said.
North Korea is very interested in reaching some sort of agreement on denuclearization so that it can grow economically with the benefit of the foreign investment closed to it now, Trump said.
The U.N. World Food Program said on Tuesday that the supply of food remained precarious inNorth Korea, where one in five children is stunted by malnutrition. More than 10 million NorthKoreans, nearly 40 percent of the population, are undernourished and need humanitarian aid, it said.
"I will tell you they're calling, wanting to go there and wanting to invest," Trump said. "At some point, when Chairman Kim makes that decision, I think he's going to unleash something that's going to be spectacular, really spectacular.
"And I think he knows it and I think that's one of the reasons that we're having very successful conversations."
(Reporting by Roberta Rampton and Steve Holland; Additional reporting by Doina Chiacu and Lisa Lambert; Editing by James Dalgleish and Peter Cooney)
© Reuters News 2018