"The number of dead will not be lower than 35," Alberto Nunez Feijoo told news radio Cadena Ser.
"There are bodies laying on the railway track. It's a Dante-esque scene," he added.
The Renfe railway company earlier said there were "several dead and injured" in the accident near the city of Santiago de Compostela, but could not immediately give a precise toll.
The train , carrying 238 passengers, had left Madrid and was heading for the northwestern town of Ferrol as the Galicia region was preparing celebrations in honour of its patron saint James.
Public television TVE repeated appeals from area hospitals for blood donations to help the injured.
"I want to express my affection and solidarity with the victims of the terrible train accident in Santiago," Prime Minister Mariano Rajoy, who is from Galicia, said in a twitter message.
The prime minsiter will visit the scene of the accident today.
A witness told radio Cadena that carriages overturned several times on a bend and came to a halt piled up on each other.
Television footage showed that four carriages had overturned and were lying on the tracks, at least one of them ripped apart with black smoke billowing.
One middle aged man wearing a white shirt had his face covered in blood as a policeman appeared to give him instructions as to where to go.
The accident happened at 8:42 pm (0012 IST) "for unknown reasons", said a Renfe spokesman.
"It was a very violent derailment," the representative of the central government in Galicia, Samuel Juarez, told radio Cadena Ser.
"We don't have any sign to allow us to speak of anything else "other than an accident, he added.
French rail operator SNCF said that derailment may have been caused by a connecting bar that came loose.
The town hall of Santiago de Compostela called off planned concerts and firework displays that had beeen planned for Thursday as part of the festivities in honour of its patron saint.
"There are psychologists available for the families of the victims and they are getting information," said a spokeswoman for the town hall.
The shrine of Saint James in the city is the destination of the famous El Camino de Santiago pilgrimage which has been followed by Christians since the Middle Ages.
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