An animal rescue organisation is offering a $5,000 reward as officials hunt a person who shot and killed a dolphin in California.

Staff from Marine Animal Rescue, a group which provides animal response and rescue services in the state, found the dead dolphin last week by the coast in the city of Manhattan Beach, in Los Angeles County.

Upon rescue and examination Dr Lauren Palmer, a veterinarian at the Marine Mammal Care Center, found that the dolphin had died from a bullet wound.

"There is NO excuse for such brutality against these beautiful animals", the organisation wrote on Facebook.

"It's just a vicious act of brutality," Peter Wallerstein, the rescue group's founder, added while speaking to NBC News.

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"We very rarely find these people but what the reward does is put them on notice."

Wallerstein said that in 30 years of animal rescue work he had never before seen a dolphin which had been shot.

In a similar case in April, a pregnant bottlefish dolphin was shot to death in southern Mississippi, according to the National Oceanic and Atmospheric Administration.

A necropsy, an autopsy for animals. revealed the dolphin had died from of a gunshot wound, with the unborn calf dying as a result of the parent's death.