Wild animals in circuses face being banned after a government consultation showed widespread public concern.
Ministers said they were "minded" to bar animals like lions and tigers from big tops in England and campaigners hope the rest of the UK will follow.
More than 90% of the 10,576 respondents said they wanted to see a total ban.
The Classical Circus Association said such a move would be "disproportionate" adding independent inspections had verified good welfare conditions.
Chris Barltrop, of the Classical Circus Association, told the BBC: "My long experience in the circus has shown me that there is not generic cruelty in the way that is described, and that circus people treat their animals very well.
"If you institute a ban just in case there is cruelty, that's a completely disproportionate reaction."
The association also pointed out that only animals born in captivity were used.
In recent years, the use of non-domesticated animals in circuses has sharply declined, a Department for Environment, Food and Rural Affairs (Defra) spokesman said.
But there are still examples of such animals performing, against the advice of organisations including the RSPCA and the British Veterinary Association (BVA).
The Defra consultation said there were currently four UK-based circuses using
non-domesticated animals including lions, tigers, kangaroos, llamas, camels,
zebras and crocodiles.
Some 95.5% of those responding to the consultation said they did not think there was any species of wild animal that could acceptably be used in circuses.
And 84% of people said they wanted to see ex-circus animals placed in zoos or sanctuaries.
Animal Welfare Minister Jim Fitzpatrick said: "I agree with the clear view emerging from the huge response to the government's consultation that keeping wild animals to perform in travelling circuses is no longer acceptable.
"We also want to make sure that circus animals are well looked after once they stop performing."
Professor Bill Reilly, BVA president, said: "Although it only affects a small number of animals at present, the BVA felt that their needs, and the needs of future animals, could not be adequately met by the environmental conditions of a travelling circus."
RSPCA wildlife scientist Dr Ros Clubb said: "Watching animals perform unnatural tricks also does nothing to educate the public or promote compassion for animals."
Any regulations or a ban would apply in England only, as animal welfare is a devolved matter.
But Defra said its ministers have kept the Scottish and Welsh administrations informed of its work.
The RSPCA is hoping a ban would be adopted by those governments.
In 2007, a group made up of representatives of the circus industry, animal welfare organisations, academics and veterinarians told Defra there was no scientific evidence to support a ban on using wild animals.
The Circus Working Group said there was "little evidence" the conditions circus animals were kept in were "better or worse" than other captive environments.