Minister for Transport Martin Cullen is to raise the problem of drivers from Northern Ireland being unaccountable for their driving in the Republic with the British government next month.
The move follows the emergence of figures showing that more than 42,000 drivers escaped penalty points in Ireland last year and the majority were from outside the country.
Under current legislation motorists from Northern Ireland cannot have penalty points imposed on them by gardaí. However, they can be charged and fined in court for traffic offences.
The latest penalty point figures also showed that of 954 drivers issued with notices for no insurance, 873 did not get points on their licences. And 38,325 drivers of the 265,515 who were caught speeding could not have points imposed.
A total of 56 motorists who were issued with careless driving notices did not receive their points, and of the 19,701 motorists found not to be wearing their seatbelts, 2,701 did not get points.
Mr Cullen has also said he is still attempting to get agreement among European transport ministers on a pan-European penalty points system. The British government currently holds the European presidency and Mr Cullen is hoping British transport minister Alistair Darling could be a powerful ally in his campaign.
However, a difficulty has emerged in that the penalty points system in Northern Ireland is separate and different to that administered in Britain.
The Garda press office has issued a statement after receiving "numerous" enquiries about holders of foreign licences. Garda Supt Kevin Donohoe asked media to "please be advised that the law and regulations governing road-traffic issues are a matter for Government".
The statement continued: "An Garda Síochána enforce the law fairly and impartially, have no input into the framing of legislation and are only one part of the justice system."
Meanwhile, the Department of the Environment, which is responsible for maintaining driving licence records, said it could not tell how many Irish citizens are currently driving in the Republic on licences they had legally acquired in Britain or elsewhere. Those drivers cannot have penalty points imposed upon them.