Smythe said the six goats and six sheep he buried died after falling into sinkholes, contracting worms or getting new feed after the grass was eaten. He said the chickens were often left out of their enclosure and that a dozen were mauled to death by dogs on two separate occasions.
Smythe said he was fired in October 2011 after arguing with his boss about the treatment of the animals.
A fourth wrangler, who didn't want to be named because she feared it could jeopardize her future employment in the industry, said another horse, Molly, got caught in a fence and ripped her leg open, suffering permanent injuries.
Dravitzki, the spokesman for Peter Jackson, said the production company reacted swiftly after the first two horses died, spending hundreds of thousands of dollars upgrading housing and stable facilities in early 2011.
"We do know those deaths were avoidable and we took steps to make sure it didn't happen again," he said.
Dravitzki said Zeppelin died of a burst blood vessel and that he knew only of three goats, one sheep and about eight chickens that had died aside from that. He said two of the goats died in a cold snap but the third, like the sheep, was old and had likely died of natural causes. He said the chicken maulings were the result of careless staff oversight.
The American Humane Association said in its report on "An Unexpected Journey" that it investigated the farm at the production company's request. Dravitzki said the company contacted the AHA after Smythe alleged mistreatment of animals.
Mark Stubis, an association spokesman, said it investigated the farm in August 2011, months after the first deaths.
"We made safety recommendations to the animals' living areas. The production company followed our recommendations and upgraded fence and farm housing, among other things," the group said.
Dravitzki said the company had already made many of the recommended changes by the time the AHA made them.
Stubis said the association acknowledges that what happens off-set remains a blind spot in its oversight.
"We would love to be able to monitor the training of animals and the housing of animals," Stubis said. "It's something we are looking into. We want to make sure the animals are treated well all the time."
Dravitzki questioned the timing of the allegations with the premiere so close but said the producers are investigating all the claims "and are attempting to speak with all parties involved to establish the truth."
He said the company no longer leases the farm and has no animals left on the property. He said he didn't know if animals will be needed for future filming in the trilogy, but added that Jackson himself adopted three of the pigs used.
Hollywood has made animal welfare a stated priority for years.
In March, HBO canceled the horse racing series "Luck" after three thoroughbred horses died during production. The network said it canceled the show because it could not guarantee against future accidents.