Prime Minister Binali Yildirim also ordered flags to fly at half mast after a car bombing near a football stadium followed by a suicide bombing at a nearby park, Anadolu said.
Interior Minister Suleyman Soylu said 27 of those killed were police and two were civilians, adding that 10 suspects had already been detained.
No group has claimed the blasts which were the latest in a year that has seen Istanbul and other Turkish cities rocked by a string of attacks blamed on Islamic State jihadists and Kurdish militants.