"According to the most recent information, 36 people have lost their lives," Yildirim told journalists at the scene of the attack, adding that "the evidence points to Daesh", using another name for the Islamic State.
The premier added that there were "many injured", without giving a figure.
Three suicide bombers opened fire at passengers with automatic rifles before blowing themselves up, Yildirim said.
He did not identify the bombers or give their nationality.
The prime minister added that the attackers had arrived at the airport by taxi. He ruled out any security failings at Ataturk, one of Europe's busiest air hubs.
Air traffic will resume at the airport from 3:00 am local time, Yildirim said.