Justice Minister Bekir Bozdag said 31 people were killed in the attack while another senior government official told The Associated Press it could climb much higher.
The senior official at first said close to 50 people had already died, but later said that the figure was expected to rise to close to 50.
The official, who spoke on condition of anonymity in line with government protocol, said as many as four militants may have been involved in the attack.
Roads around the airport were sealed off for regular traffic after the attack and several ambulances could be seen driving back and forth. Hundreds of passengers were flooding out of the airport and others were sitting on the grass, their bodies lit by the flashing lights of the emergency vehicles.
Twelve-year-old Hevin Zini had just arrived from Dusseldorf with her family and was in tears from the shock.
She told The Associated Press that there was blood on the ground and everything was blown up to bits.
She says she hid under the counter for some time. Favish says passengers were ushered to a cafeteria at the basement level where they were kept for more than an hour before being allowed outside.
Another Turkish official said attackers detonated explosives at the entrance of the international terminal after police fired at them.
The official, who spoke on condition of anonymity in line with government protocol, said the attackers blew themselves up before entering the x-ray security check at the airport entrance.
Two South African tourists, Paul and Susie Roos from Cape Town, were at the airport and due to fly home at the time of the explosions and were shaken by what they witnessed.
"We came up from the arrivals to the departures, up the escalator when we heard these shots going off," Paul Roos said. "There was this guy going roaming around, he was dressed in black and he had a hand gun."
The private DHA news agency said the wounded, among them police officers, were being transferred to Bakirkoy State Hospital.
