"Our sky is our sky, not the USA's sky," acting Iraqi Interior Minister Adnan al-Asadi told The New York Times.
Iraqi officials say the U.S. government needs Iraqi approval to use the drones.
Asadi, Ali al-Mosawi, a top adviser to Prime Minister Nouri al-Maliki, and national security adviser Falih al-Fayadh all said they weren't consulted by U.S. officials about use of the drones.
A month after the last U.S. troops left Iraq, the State Department relies on the drones as part of its effort to take over functions the military had performed, the Times said.
But some senior Iraqi officials view the program as what the newspaper called an "affront to Iraqi sovereignty."
The State Department confirmed the "unarmed aerial vehicles" program without mentioning Iraq, saying in a statement: "The department does have a [UAV] program. The UAVs being utilized by the State Department are not armed, nor are they capable of being armed."
The State Department drones also are much smaller than Predator and Reaper drones used by the Pentagon and the CIA to attack militants in Pakistan, Yemen and Somalia, with wingspans as short as 18 inches, compared with 55 feet for the Predators.
In an online prospectus in September, the State Department said the surveillance drone program is designed "to provide real-time surveillance of fixed installations, proposed movement routes and movement operations," referring to American convoy movements, and improve security "in high-threat or potentially high-threat environments."