There was a "high probability" that Islamic State was to blame, he added.
The government has now vowed to increase security at the Syrian border.
"What`s necessary will be done against whomever responsible for (the attack)," said Mr Davutoglu.
"This is an attack that targeted Turkey," he added.
He rejected claims that the ruling Justice and Development Party (AKP) had not done enough to combat IS militants, saying the government had "never tolerated any terrorist group".
A cabinet meeting on Wednesday will examine additional security measures along the border with Syria.
Officials initially suggested the bomber may have been female, but local media outlets have named a man in connection with the attack.
All rallies and marches in the city of Sanliurfa, where Suruc is located, have now been banned.
The governor of the city said the measure was aimed at preventing "undesirable occurrences".
The funerals of some of the victims have already taken place, but many relatives are still awaiting news of their loved ones.
The youth activists, who were mainly university students, were holding a news conference when the bomb ripped through the cultural centre. They had been planning to travel to Syria to help rebuild the town of Kobane.
Social media images showed the group, who were members of the Federation of Socialist Youth Associations, relaxing over breakfast a few hours before the noon blast.
Mr Davutoglu is expected to visit the scene of the massacre later on Tuesday.
Suruc is home to many refugees who have fled fierce fighting between IS and Kurdish fighters in nearby Kobane.
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