A critically endangered native sea lion has been killed by a gunshot wound in the South Island.

Members of the public found the male New Zealand sea lion (rapoka) - one of just 10,000 remaining - in Jack's Bay in the Catlins, between Balclutha and Invercargill.

Department of Conservation spokesperson Chris Bowen said it died from serious blood loss as a result of a lung haemorrhage caused by a bullet. It was otherwise in good health.

"The shooting of an endangered animal is hard to comprehend. There are only about 10,000 New Zealand sea lions left so losing one in this way is particularly tragic," Bowen said.

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"It would have been a slow, painful death."

The sea lion was alive when it was discovered. DOC was contacted but it later died of its wounds.

The New Zealand sea lion population is in decline, and it is one of the rarest species in the world. Archaeological evidence suggests the sea lions were once found along the entire length of the country, but they are now only found at the tip of the South Island.

They were killed for their pelts for more than 20 years in the 19th century until there was no longer a large enough population to support the trade.

Males are brown to black, can be up to 3.5 metres in length and 400kg. Females are lighter in colour, and get up to two metres and 160kg. They are generally confident with people and can get quite close.

Anyone found guilty of injuring or killing a season lion can face up to five years' imprisonment and a fine of up to $250,000.

DOC is urging anyone with information about this to contact the Murihiku/Invercargill DOC office on 03 211 2400 or the DOC hotline 0800 362 468.

The police have been notified of the incident.