The Garda Commissioner says it is not possible to close a loophole in the Covid-19 laws.
A gap in the legislation means day-trippers from Northern Ireland do not have to abide by movement restrictions.
The regulations are underpinned by the Health Act, which only applies to residents of the State.
Commissioner Drew Harris says there is close cooperation with the PSNI on the matter.
He said: “Those who are engaged in non-essential travel, who in effect of this expression day-tripping, into this jurisdiction - they may have breached the law as it is in Northern Ireland.
“The Police Service of Northern Ireland are obviously responsible for that piece of enforcement.
“The same way as we would challenge those who are engaged in non-essential travel who might travelling north into Northern Ireland as well."