Turkey's Justice Ministry and the offices of its ruling AK Party were also attacked with homemade bombs and a shoulder-fired missile in the capital Ankara on Tuesday, but no one has claimed responsibility for the attacks.
The explosions came ahead of Thursday's expected ceasefire call by jailed Kurdish militant leader Abdullah Ocalan, who has been in talks with state officials to try to end a three-decade conflict that has killed some 40,000 people.
The ceasefire call, expected to coincide with the Kurdish New Year, would be a major step in what is shaping up to be the most serious bid yet to end Turkey's conflict with the Kurdistan Workers Party (PKK) militants.
An unidentified assailant threw a small bomb into the garden of a local state official's offices in the Maltepe district of Istanbul on Wednesday, broadcaster NTV said on its website. Separately, a police team defused explosives left in front of a cultural centre on the same side of the city.
As well as Kurdish militants, far-left groups, ultra-nationalists and Islamic radicals have also carried out attacks in Turkey in the past.
The AK Party attack shattered windows on the seventh floor of its headquarters, where Prime Minister Tayyip Erdogan has an office, while two devices exploded outside the Justice Ministry several kilometres (miles) away.
A large Turkish flag was hung from the front of the AK Party building on Wednesday, concealing the place where the missile struck. Erdogan, who left Ankara earlier on Tuesday for an official visit to Denmark, has been briefed on the attacks.
A member of the Revolutionary People's Liberation Party-Front (DHKP-C) leftist group blew himself up at an entrance of the US embassy on Feb. 1, killing a Turkish guard.
Turkish police have detained more than 100 people in a series of operations against the DHKP-C since January, most recently seizing 12 people on Tuesday.
The DHKP-C, listed by Turkey and the United States as a terrorist organisation, has carried out attacks in the past in retaliation for arrests of its members. — Reuters