WASHINGTON—Iran so far has refused to allow United Nations inspectors to interview key scientists and military officers to investigate allegations that Tehran maintained a covert nuclear-weapons program, the head of the U.N.’s nuclear watchdog said in an interview Wednesday.

Iran’s stance complicates the International Atomic Energy Agency’s probe into Tehran’s suspected nuclear-military program—a study that is slated to be completed by mid-December, as required by the landmark nuclear agreement forged between world powers and Iran on July 14 in Vienna.

The IAEA and its director-general, Yukiya Amano, have been trying for more than five years to debrief Mohsen Fakhrizadeh-Mahabadi, an Iranian military officer the U.S., Israel and IAEA suspect oversaw weaponization work in Tehran until at least 2003.

Mr. Amano said Tehran still hasn’t agreed to let Mr. Fakhrizadeh or other Iranian military officers and nuclear scientists help the IAEA complete its investigation. The Japanese diplomat indicated that he believed his agency could complete its probe even without access to top-level Iranian personnel.

“We don’t know yet,” Mr. Amano said about the agency’s interview requests. “If someone who has a different name to Fakhrizadeh can clarify our issues, that is fine with us.”