The incident occurred at around 1.00 p.m. local time (1000 GMT) in the Sariyer district, on the city's European side.
Istanbul Chief Public Prosecutor Hadi Salihoglu said in a statement that the man jumped on security guards to coerce them into helping him meet President Recep Tayyip Erdogan.
Erdogan was not in the building at the time.
The as-yet-unidentified man told security staff: "Help me meet with Erdogan and open the doors," Salihoglu's statement read.
The man then snatched a weapon from a security guard, firing shots at police before turning the gun on himself, a presidential statement read.
No security personnel were injured during the incident.
An investigation is underway.
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