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...