WASHINGTON—The U.S. threatened to slap sanctions on countries that don’t cut oil imports from Iran to “zero” by Nov. 4, part of the Trump administration’s push to further isolate Tehran both politically and economically, a senior U.S. State Department official said.

Buyers of Iranian crude had expected the U.S. would allow them time to reduce their oil imports over a much longer period, by issuing sanctions waivers for nations that made significant efforts to cut their purchases. That expectation was partly based on previous...