The fire, which officials said was likely caused yesterday by an electrical fault, raced through the building's wooden interior as panicked victims tried to jump from windows to safety.
Officials expressed concern that many of the dead were killed after they were unable to open a closed fire door to escape the top floors of the building.
Images showed scenes of devastation as emergency services arrived to tackle the fire at the dormitory building, parts of which were turned into a blazing wreck and whose roof collapsed.
"According to initial findings, we believe the fire was caused by electrical fault," he said.
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The Dogan news agency specified that all 11 of the schoolchildren killed were girls. Their identities have yet to be disclosed but they were also said to be 14 or under.
The disaster took place in the town of Aladag north of Adana city, one of the biggest urban centres in the south of Turkey.
Demirtas said some terrified schoolgirls were injured after jumping out of the window to escape the flames. He added that none of the injuries were serious condition.
The governor said the fire at the private schoolchildren dorm broke out at around 19:25 (1625 GMT) and it was brought under control some three hours later.
Demirtas declined to comment on claims that fire escape stairs were locked and students were unable to use them.
But Adana city Mayor Huseyin Sozlu said: "It appears that the fire escape stairs door was locked. Children could not open it. Bodies were found there," he said.
"From tomorrow the governor's office will start an investigation."
He said the children were aged between 11-14.
Students trapped on the second and third storeys of the building who could not flee outside, were killed in the fire, the Dogan news agency said.
The fire spread rapidly because of the building's wooden interior and carpeted floor, officials said.
Aladag district's mayor Mustafa Alpgedik, quoted by the Dogan news agency, said the fire erupted on the ground floor and then the flames spread because the third floor was wooden.
In an agonising wait, families who could not see their children stood outside in tears, Dogan added.
The dorm had a capacity for 54 students and was open to both secondary and high school students. Demirtas said it was a private dormitory with 34 students in residence.
Fires are frequent in Turkey due to antiquated and often wooden buildings and faulty electrics. But a disaster of this magnitude is highly unusual.
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