The Government has been urged to set up its own screening programme to allow free movement of pets between the State and the Continent rather than rely on the British authorities to make the decision.
The call came from Mr Ciaran O'Donovan, chief executive of the Irish Society for the Prevention of Cruelty to Animals (ISPCA), who described the new situation as "daft".
The Cabinet decided last week to allow animals which had satisfied the British pets passport scheme to be allowed into Ireland.
Under the British system, which will operate on a pilot basis for one year, pets must be vaccinated, microchipped, treated for parasites and given a clean bill of health by a vet before entering the UK through selected ports.
However, the Government decision will not allow pets coming from mainland Europe and which satisfy the British regulations to be imported directly into the Republic.
Mr O'Donovan said that this did not appear to be a sensible decision and he urged the Government to set up Irish control points to allow animals to be imported directly into the State.
Mr Mike Woods, a veterinary surgeon, who is president of the Companion Animals Association, said he would like to have seen a scientific committee set up in the State to examine the issue before a decision was taken.
"I would not be worried so much about rabies but [about] other diseases which we have never had in this country or in Britain," he said.
The British regulations came into force at the beginning of this month.