MANILA (Reuters) - U.S. Secretary of State Mike Pompeo said on Thursday that the United States and North Korea could hold further meetings after a second summit between President Donald Trump and North Korean leader Kim Jong Un in Vietnam failed to yield an agreement, but there was no plan to do so immediately.

U.S. Secretary of State Mike Pompeo (2nd L) attends a working lunch alongside President Donald Trump (L) during a meeting with Vietnamese Prime Minister Nguyen Xuan Phuc (unseen) at the Office of Government Hall in Hanoi, Vietnam, February 27, 2019. REUTERS/Leah Millis

“We haven’t set a date,” Pompeo told reporters on a flight from Vietnam to the Philippines. “My sense is it will take a little while. We’ll each need to regroup a little bit. But I’m very hopeful that Special Representative (Stephen) Biegun and that team will get together before too long,”

“But we’ll see ... there has to be a reason for the conversations,” Pompeo said.

Biegun, who led working-level negotiations with his North Korean counterpart in the run-up to the Hanoi summit, was on the plane with Pompeo, but did not speak to reporters.

“There has to be a theory of the case about how to move forward,” Pompeo said. “I’m confident that there is one. I’ve seen enough congruence between what the two sides are trying to accomplish. I saw the goodwill between the two leaders, and so I hope we can come up with a plan.”

Pompeo said the two sides had “cleared away a lot of brush” in working-level talks in the past 60-90 days.

“And then we were hoping we could take another big swing when the two leaders got together. We did. We made some progress. But we didn’t get as far as we would have hoped ...”

Trump said earlier he walked away from a nuclear deal at his summit with Kim in Vietnam on Thursday because of unacceptable demands from the North Korean leader to lift U.S.-led sanctions.

Pompeo said Kim reiterated he was fully prepared to denuclearize and to maintain a freeze on nuclear and missile testing, while Trump said he was still committed to not conducting joint military exercises with South Korea.

“So there’s still a basis for believing that we can move forward,” Pompeo said, while adding there was “still a lot of work to do” on achieving denuclearization.

Pompeo declined to give details of the negotiations but when asked whether the North Korean demand for full sanctions relief was a longstanding one in the talks or something sprung on the U.S. side at the last minute, he replied:

“I will say we haven’t been surprised by much of anything.”