The massive car bomb struck five buses carrying military service personnel when it stopped at a red traffic light in the centre of the capital on Wednesday evening. Sixty-one people were wounded.
It was latest in a string of deadly strikes that have rocked Turkey since last summer and one of the deadliest assaults targeting the military in the NATO member state in recent years.
Also Thursday, at least six soldiers were killed in an attack on their convoy in southeastern Turkey blamed on Kurdish militants, security sources said.
"It has with certainty been revealed that this attack was carried out by members of the terrorist organisation in Turkey in cooperation with a YPG member who infiltrated from Syria," Davutoglu told reporters.
"The attack has direct links with YPG."
He said the bomber was a Syrian national named Salih Necar and that nine people had been detained over the attack.
Davutoglu vowed to make the culprits "pay a price," saying Turkey would take any kind of measure on its border including self-defence.
Davutoglu said 70 fighters had been killed in the strikes.
Turkey both considers both the PKK and YPG to be terror groups, in contrast to the United States which only classifies the PKK as a terror organisation and works closely with the YPG as an effective force fighting jihadists in Syria.
The attack struck the heart of power in the Turkish capital in an area where the headquarters of the army, the parliament and prime minister's offices are in close proximity.
Police identified the bomber from fingerprints taken from refugees who crossed the border to escape the war in Syria, the strongly pro-government Yeni Safak and anti-government Sozcu daily said.
The YPG and its political wing the Democratic Union Party (PYD) deny being PKK branches and argue they have no interest in attacking Turkey.
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