Muammer Guler told reporters that the unidentified gunmen had driven up to the U.S. mission and opened fire on a police guardpost. Three of the gunmen died at the scene, and a fourth escaped in the vehicle, he said.
TV footage showed four bodies on the ground outside the building. One police officer reportedly died at the scene, while another two died later in hospital.
Guler said a fourth police officer was injured in the attack, along with a bystander.
Eyewitnesses told reporters that a white car pulled up outside the building at around 11:00 a.m. (08:00 GMT). A man stepped out, and approached the guardpost, concealing a firearm in his coat, before shooting an officer in the head.
The U.S. Embassy said that no consular personnel were injured in the attack.
The city governor said investigators are working to identify the gunmen, and to find out whether they belonged to a terrorist network. The search for the fourth accomplice is ongoing.
