WASHINGTON—Secretary of State Mike Pompeo on Thursday will leave for North Korea to engage in the first high-level talks on eliminating Pyongyang’s nuclear weapons and programs since the Singapore summit in June, U.S. officials said.

The trip comes amid growing concerns that Washington and Pyongyang may not share the same goals on the pace and scope of efforts to denuclearize the Korean Peninsula and reports that North Korea is proceeding with its weapons programs.

Mr....