One police officer was killed in the shootout, according to local media.
The police station bomb attack injured 10 people, including seven civilians. The blast caused a fire in the building and damaged neighboring houses.
Also on Monday, two unidentified gunmen, a man and a woman, opened fire at a US diplomatic mission in the northernmost district of Istanbul.
The incidents come a day after the United States deployed six F-16 fighter jets to the southern Turkish base of Incirlik to conduct airstrikes against the Islamic State (ISIL) jihadist group in neighboring Syria.