President Erdogan told reporters on Sunday that Turkey would fight "the scourge of terrorism to the end", and promised that the attackers would pay a "heavy price".
The vehicle bomb and suicide attack killed eight civilians and 36 police officers stationed in Beşiktaş, on Istanbul's European side, Recep Akdağ, the health minister, said.
Turkey's Interior Ministry said 568 people have been detained across 28 cities since Monday on account of their alleged affiliation with the Kurdistan Workers Party, or PKK.
Deputy Prime Minister Numan Kurtulmus said initially that that the outlawed PKK was likely at fault and that said 13 people have been arrested so far in connection with the bombings.
Hours after that claim, Turkish warplanes carried out air strikes against PKK targets in northern Iraq, destroying a base of the fighters and surrounding gun positions and shelters, an army statement said.
Soylu said 136 people remained hospitalized after the attack, including 14 under intensive care.
Police arrive at the site of an explosion in central Istanbul, Turkey, December 10, 2016.
Prime Minister Binali Yildirim has ordered flags to be flown at half-staff.
The PKK as a practice has targeted security forces and avoided attacking civilians, whereas ISIS has readily attacked civilians and sought to cause as many deaths as possible. Two explosions hit central Istanbul on Saturday night, injuring 20 people, the authorities said.
The PKK is widely known for periodic attacks on Turkish security forces.
Turkey launched "Operation Euphrates Shield" four months ago in a bid to push Islamic State militants away from its border in northern Syria and prevent Kurdish militia groups from seizing territory in their wake.
Istanbul has been the scene of several bombings this year, including a June attack at Atatürk Airport that killed more than 40 people.
Turkey on Tuesday continued to round up people accused of involvement in an armed Kurdish movement labeled as a terrorist organization in the country.