Authorities in Alaska have launched an official investigation, as polar bears are listed as threatened with extinction under the US Endangered Species Act and cannot be hunted under the Marine Mammal Protection Act.

The US Fish and Wildlife Service and the oil company revealed that the female bear was shot in early August and died of its wounds about 11 days later. It was monitored by BP guards until it died on a nearby island.

Bruce Woods, a US Fish and Wildlife Service spokesman, said: “We’re taking this investigation very seriously and hope to find out what happened.”

A BP spokesman said the bear had been killed by mistake, since the guard thought he was shooting beanbags rather than a “cracker round” at the animal, after it was spotted prowling towards employee housing at the Endicott field.

Companies are allowed to conduct “non-lethal harassment” of polar bears threatening humans, but not permitted to shoot to kill.

BP recorded 541 polar bear sightings between 2005 and 2010, but this is the first time an animal has been fatally shot.

The investigation is a setback for BP’s attempts to rebuild its reputation in the US, after the Gulf of Mexico oil spill harmed its environmental credentials.

Polar bears live on Alaska’s Arctic coastline, sometimes make their way on to oil fields on the North Slope region. The bears are monitored by the field operators when they venture near to human habitation.

Malcolm Graham-Wood, analyst at VSA Capital, said: “BP spent a lot of time last year firefighting following Macondo, you would have thought that they might have tried to keep their head down stateside.”

BP’s share price closed 0.2 higher at 386.3p on Thursday, having recovered since its depths just above 300p at the height of the oil spill, but around 25pc lower than this year’s peak of 509p.