The bureau's law enforcement officials are investigating.
"The BLM is serious about enforcing the 1971 Wild Horse and Burro Act that protects wild horses on the range," said the bureau's Idaho state director Steve Ellis.
"The act clearly states that it is a federal crime for any person to maliciously cause the death of any wild horse, and we want to find whoever is responsible."
The penalty for shooting or harassing wild animals on federal land is a fine of up to $US100,000 and one year in jail.
The bureau has successfully prosecuted cases in the past, with jail time served.
"We care a great deal for the welfare of these animals and want to prevent this from happening in the future," Ellis said.
"I am hopeful the public will be able provide us information that will help in this investigation."