President Recep Tayyip Erdogan said after Saturday's attack in Gazantiep that the bomber was 12-14 years old.
Turkey has linked the bomber to so-called Islamic State (IS), but Mr Yildirim said "a clue has not yet been found concerning the perpetrator".
His statement came as Turkey's military targeted IS militants in Syria.
Television reports said howitzers had been used against IS near the border town of Jarablus.
Turkish artillery had also hit US-backed Syrian Kurdish YPG positions north of Manbij in Syria.
A coalition including YPG has been pushing IS out of Syrian towns, including Manbij, recently.
Turkey views the YPG as an extension of the Kurdistan Workers Party (PKK), a Turkish-Kurdish rebel group fighting for autonomy since the 1980s.
Speaking to reporters after a cabinet meeting on Monday, Mr Yildirim said the earlier statement identifying the attacker as a child was a "guess" based on witness accounts.
Twenty-nine victims of the attack, which took place on Sunday, were under the age of 18, reports said, with one official saying 22 were under the age of 14.
Thirteen of those killed were women, Turkish media said. Sixty-six people are still in hospital, 14 of them in a serious condition, Dogan news agency reported.
One woman lost four children in the attack, the Haberturk newspaper reported. Emine Arhan told the title "if it wasn't for my only surviving child, I would have killed myself".
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