Speaking on Saturday at the funeral of two police officers killed in Thursday's blasts, Erdogan said that it was a matter of shame for Turkey that its own citizens were responsible for the attacks.
"We have lost four terrorist who were our citizens," said Erdogan.
Turkish media have named two of the four suspected bombers: Azad Ekinci and Feridun Ugurlu, both from southeastern Turkey.
Twenty-seven people were killed and over four hundred injured in Thursday's attacks on the British consulate and HSBC bank in Istanbul.
A group suspected of links to al-Qaida - the Abu Hafz al-Masri Brigades - has claimed responsibility for the attacks, which followed the similiar bombings of two synagogues in Istanbul last Saturday.
Another group linked to al-Qaida - The Great Eastern Islamic Raiders Front (IBDA-C) - claimed responsibility for the synagogue bombings, which left 25 dead and more than 200 injured.
One Turkish newspaper has reported police detained 18 people from three Istanbul districts, in connection with the blasts.
The Hurriyet newspaper says all police leave has been cancelled indefinitely.
Many Turks are taking to the streets to stage a silent protest against the bombings that has left the country in shock.
Although most of the victims caught up in Saturday's synagogue blasts were Muslims, trade unions have called on people of all faith to protest against the attacks.
Next week sees the beginning of the Muslim festival of Eid al-Fitr marking the end of Ramadan. The city should be gearing up for celebrations, but instead many residents are feeling anxious about the possibility of more attacks.