"We have an unacceptable situation of absolutely sickening cruelty acts," Denormandie told France Info radio.
"I hear the fear, the concerns, the disarray of horse owners," he said, adding that a toll free number was being made available to horse owners from Wednesday morning.
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Horses have been found with ears cut off, eyes gouged out and genitals mutilated. Police say they have no idea why; theories include a satanic rite, macabre trophy hunt or internet challenge.
A 50-year-old jobless man arrested on Monday in eastern France as part of the investigation was released without charge, a police source said on Tuesday.
