Vaccinated pets from 28 countries outside the European Union will be allowed to enter the State through the UK without quarantine from the end of this month.
Dogs and cats from Australia, New Zealand, Japan, Singapore, Jamaica and other rabies-free countries will be allowed into the UK once they have been fitted with a microchip, vaccinated against rabies and blood-tested to ensure the injections worked.
As there is no quarantine between the UK and the State, pets which pass UK monitors will be permitted to travel here.
A spokesman for the Department of Agriculture said it was hoped a similar scheme would be introduced for direct access to the State this year once an evaluation of the UK scheme had been reviewed and Government approval had been sought.
Quarantine restrictions were first lifted a year ago in the UK on pets originating in 22 western European countries.
The British government is reviewing lifting quarantine restrictions on animals travelling from the US and Canada, where rabies exists. Restrictions may also be lifted on other pets, including mice, rabbits and gerbils.
Some 12,500 pets have entered the UK through the new scheme, with only six pets failing the monitoring system.
The Department of Agriculture said it did not know how many pets had entered the State from other countries through the UK under the scheme.
Mr Ciaran O'Donovan, the chief executive of the Irish Society for the Prevention of Cruelty to Animals, said he supported the introduction of the scheme.