The killer whale responsible for the death of a trainer during a live show is suffering from a bacterial infection that could eventually kill him, SeaWorld officials say.

The infection in Tilikum's lungs has been resistant to treatment so far, the Florida theme park said.

The orca - which has been at SeaWorld in Orlando for 23 years - is lethargic and veterinarians and trainers are attempting to manage the infection and make sure he is comfortable.

Staff veterinarian Dr Scott Gearhart said in a video posted on the park's blog: "It's extremely difficult to treat.

"I wish I could say I was tremendously optimistic about Tilikum and his future but he has a disease that is chronic and progressive and at some point might cause his death."

Tilikum, nicknamed Tilly, is one of the park's biggest and best-known attractions and is believed to be aged around 35, which is advanced in years for male killer whales.

In 2010 Tilikum grabbed trainer Dawn Brancheau after a "Dine With Shamu" show and pulled her into a pool, killing her.

The killer whale was involved in the deaths of two other people.

In 1991, a part-time trainer at Sealand of the Pacific in British Columbia slipped into a pool holding Tilikum and two other orcas.

They submerged her and dragged her around the pool.

The park closed shortly after the incident, and Tilikum was moved to SeaWorld Orlando.

Eight years later, a man who had trespassed into SeaWorld Orlando after the park had shut was found dead in the orca's pool.

A documentary, Blackfish, chronicled Tilikum's life and argued that killer whales became more aggressive to humans and each other when kept in captivity.

The film sparked criticism of SeaWorld by animal rights activists.

In November, the company said it planned to phase out its signature killer whale show.

Ingrid Newkirk, president of animal rights group PETA, greeted the news of Tilikum's illness with skepticism.

"When SeaWorld feels that it must make a statement about Tilly's ill health, PETA bets that it's anticipating someone is about to blow the whistle about his illness, or reveal that he's dying and that the people who have exploited him to line their pockets all these years know that," she said.

"Since SeaWorld can no longer capture orcas from the wild, it has used Tilikum as its chief breeding machine, churning out more performers for a miserable life that no one would ever willingly choose," she added.