"This is an extraordinarily difficult time for the SeaWorld parks."
Jim Solomons of the Orange County Sheriff's office earlier said Brancheau died after slipping into the tank.
"She apparently slipped or fell ... and was fatally injured by one of the whales," he said. "This appears to be an accidental death, it's a tragic death."
Tilikum, whose name means "friend" in the Chinook Jargon language spoken among native Americans in the Pacific Northwest, is among the killer whales, dolphins and seals whose shows have made SeaWorld popular.
But he has been involved in previous human deaths, including in 1991 when a part-time trainer at the Sealand of the Pacific facility in Canada was killed in his tank, according to the Humane Society of the United States.
In 1999, after being shipped from Canada to Orlando, the whale was blamed for the death of a man who had apparently stayed in SeaWorld after closing.
The Humane Society said the man jumped into Tilikum's tank and was found dead the next morning, his naked body covered in scratches that suggested he had been dragged around the bottom and sides of the tank.
A witness told CNN that Tilikum attacked the trainer as she showed him off to park visitors following the Dine with Shamu show.
"He just took off like a bat out of you know what, took off really fast and came back around to the glass, jumped up, and grabbed the trainer by the waist and started shaking her violently," witness Victoria Biniak said.
"The sirens were going off. People were running out. I've never seen so many SeaWorld employees come out of the woodwork."
Another witness told CNN that the whales in the tank had begun ignoring the trainers.
"We could tell this whale was not in a good mood at all. We literally could tell it was not cooperating," said the unnamed witness.
Though killer whales, also known as orcas, are a common attraction at entertainment parks, they are known for aggressive "play" and behavior in the wild, including batting seals or dolphins back and forth.
They are huge creatures -- Tilikum weighs at least 11,000 pounds (five tonnes) -- and "are among the most curious of all whales, with a great tendency to 'play' and to manipulate objects," says SeaWorld's website.
Tilikum was captured in November 1983 off the coast of Iceland and is one of several killer whales on display at the Orlando park, which was partially closed down after the trainer's death.
SeaWorld's website said its shows involving killer whales in Orlando and in San Diego, California, have been suspended.
Animal rights group People for the Ethical Treatment of Animals released a statement saying the death was a "tragedy that didn't have to happen."
"For years, PETA has been calling on SeaWorld to stop confining oceangoing mammals to an area that to them is like the size of a bathtub, and we have also been asking the park to stop forcing the animals to perform silly tricks over and over again," it said.
