The series of assaults, which authorities suggested were the work of ultra-leftists, come as the nation is reeling from an unprecedented series of attacks and bombings.
The shooter opened fire on officers in a car in the Esenyurt district of Istanbul, the Dogan news agency said. The assailant left a hand grenade before running away when officers shot back. No injuries were reported.
The attack came in the same area where the gunman blamed for the New Year shooting on an elite nightclub in Istanbul was arrested.
No one was killed or injured in any of the three attacks, local media said.
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Images in Turkish media showed an unexploded rocket which had become stuck in a framed text of the Turkish national anthem inside the AKP offices.
No group claimed responsibility for the attacks but authorities suggested the outlawed ultra-leftist Revolutionary People's Liberation Party-Front (DHKP-C) could be to blame.
Turkey's Prime Minister Binali Yildirim said there was speculation that a "leftist terror group" was the culprit but said it was not clear which one, referring to the DHKP-C and another.
The attacks happened as the Turkish parliament in Ankara was voting on a draft bill to expand President Recep Tayyip Erdogan's powers, which was approved in the early hours of Saturday.
EU Affairs Minister Omer Celik said on Twitter such attacks target people and security services, but they also target "politics and tr(y) to influence decision making mechanisms".
After multiple bombings in 2016 blamed on jihadists and Kurdish militants, the new year began with the bloody attack on Istanbul's Reina club which killed 39 people.
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