But Pompeo was still referring to the meeting as a "proposed summit" and said he couldn't say for sure whether it might be announced after a top North Korean official he's been meeting with hand-delivers a letter from Kim to the president on Friday.
The top U.S. diplomat has been in New York for two days of meetings with his counterpart, Vice Chairman of the Central Committee Kim Yong Chol, North Korea's point man on nuclear negotiations and former spy chief. The two met to hammer out final details of the summit's agenda and to determine whether or not it could be a success.
"It does no good if we're in a place where they don't think there's real opportunity to place them together," Pompeo said during a news conference in New York Thursday. He added that he still does not know whether the summit will happen, but the two sides had made "real progress in the last 72 hours towards setting the conditions" to make it successful.
Kim Yong Chol and his delegation will now head to Washington to present a letter from Kim Jong Un to Trump in person, a senior State Department official confirmed. They will not travel with Secretary Pompeo, but he will also attend the meeting, although it's unclear where it will take place.
Trump told reporters earlier on Thursday that he "believe[d] they'll be coming down to Washington on Friday, and a letter is going to be delivered to me from Kim Jong Un. So I look forward to seeing what's in the letter."
At the crux of negotiations now is persuading North Korea that it does not need nuclear weapons for its security and that the weapons program, in fact, makes them less secure by threatening the U.S. and its allies, Pompeo said. The U.S. has been "consistent" in its demands for "complete, verifiable, irreversible denuclearization," he added – and he told ABC News Chief Global Affairs Correspondent Martha Raddatz that the regime could be on the cusp of agreeing to that in a "strategic shift."
"Martha, I have had a chance to meet Chairman Kim Jong Un twice and now Kim Yong Chol three times. I've spent a great deal of time with each of them. I believe they are contemplating a path forward where they can make a strategic shift, one that their country has not been prepared to make before," he said.
But he warned that there will likely be bumps in the road ahead, sharing that he's had "difficult conversations with them" and "they've given it right back to me, too," he said with a smile.
That means that the summit is still touch-and-go, but it was unclear from Pompeo what's still standing in the way.
"One not ought to be either surprised or frightened or deterred by moments where it looks like there are challenges and difficulties, things that can't be bridged. Our mission is to bridge them so that we can achieve this historic outcome."
Pompeo and Kim Yong Chol met first for dinner on Wednesday night at a residence leased by the U.S. government on the east side of Manhattan. They shared a meal of filet mignon and were seen toasting and shaking hands in photos released by the State Department. A senior State Department official said the dinner was about getting to know each other as the talks move forward.
That was followed by the real work Thursday, with meetings in the same apartment starting at 9 a.m. After just two hours and 20 minutes, the meetings ended earlier than expected – but Pompeo said it was a good sign.
"We had a set series of items that we wanted to make sure we covered, topics we made sure we were clear on in terms of what our expectations were for them and their expectations in return for us. We achieved that," he said.
As he's said many times before, Pompeo noted the administration had its eyes wide open – but hoped that there could be a "historic" outcome.