One suspect was netted on Tuesday, hours after the attack.
Emerging from a meeting on security in Istanbul, Davutoglu told reporters that after a detailed investigation the authorities have detected the assailant's link with Islamic State (IS) and revealed some secret actors and important elements behind the attack.
"The assailant's link to IS has been determined but IS is an intermediary organisation," the prime minister said.
Davutoglu claimed that some countries are trying to drag Turkey into a fire circle.
"We will reveal all these ties behind IS and we won't let Turkey be dragged into this circle," he added.
The prime minister vowed to reveal the "real actors" behind the IS which Turkey has said was behind last year's bombings in the southeastern city of Suruc and the capital Ankara, and now in Istanbul.
He also confirmed that the Istanbul bomber entered into Turkey as a refugee.
Earlier in the day, Turkish Interior Minister Efkan Ala said that nine of the 10 killed were reportedly German tourists.
The minister said 17 others were injured, adding nine of them are German citizens, one from Peru, the rest from Norway. A total of 11 are undergoing treatment and two of them are critical, Ala said.
The Turkish minister assured foreigners visiting the country that the government has taken necessary measures to ensure security.