Secretary of State Mike Pompeo said Tuesday he made “real progress” on his visit to North Korea and now believes the goal of verifiable denuclearization is within reach.

“While there’s still a long way to go and much work to do, we can now see a path to where we’ll achieve the ultimate goal, which is the full and final verified denuclearization of North Korea,” Mr. Pompeo told reporters.

He made the comments at the White House after a lunch with President Trump.

Mr. Pompeo said he would announce “in short order” a second summit between Mr. Trump and North Korean leader Kim Jong-un, following up on their breakthrough spring meeting in Singapore.

Mr. Trump told reporters of the second summit, “we’re setting that up right now.” He said they are discussing three or four possible sites.

“Singapore was fantastic, but we’ll probably do a different location,” the president said.

Mr. Trump said the North Korean leader is anxious for international sanctions to be lifted and to “get on” with economic development in the isolated communist nation. But the U.S. is requiring verifiable dismantling of Pyongyang’s nuclear arsenal first.

“We haven’t removed sanctions,” the president said. “I’d love to remove them, but we have to get something for doing that. I think that the country of North Korea is going to be a very successful country. I think it’s going to be incredibly economically successful. And I want to make it that way. 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. I think he wants to get on with it.”

Mr. Trump said he envisions eventual meetings with Mr. Kim in the U.S. and in North Korea.

“That’s a two-way street — on their soil, also,” Mr. Trump said. “I think it’s going to be great.”

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