Regional government head Alberto Nunez Feijoo confirmed 35 bodies were found at the crash scene, El Pais reported, adding the death toll could rise.
Dozens more passengers were injured, the Spanish newspaper said.
"The scene is a mess," one unidentified passenger told the newspaper. "People were wounded and bleeding next to me."
A large crane was moved into place to move the wrecked rail cars as the search went on for more victims.
The newspaper said about 238 people were on the train when it derailed.
Charlize Theron not engaged to Sean Penn 'yet'
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend