The group that represents Garda sergeants and inspectors say there needs to be an all-Ireland approach when policing the coronavirus.
It has emerged there is a loophole in the law, meaning people visiting the Republic of Ireland from Northern Ireland and not staying the night are not affected by the restriction rules.
It means people from the North travelling here on day trips cannot be arrested due to a gap in the new coronavirus legislation.
President of the Association of Garda Sergeants and Inspectors (AGSI), Cormac Moylan, explained the issue to Newstalk Breakfast.
"We're unable to use these powers for people coming from Northern Ireland who are travelling beyond 2km from their place of residence.
"But as the residence is not in this jurisdiction it creates an issue for the members - particularly in the border counties... in Donegal, Cavan, Monaghan and Louth."
"It is important to say that the vast, vast majority of instances, people are understanding and adhering to instructions and the guidance that's been given".
"That's what we're hearing from our members that are out there".
"As it stands we can't return visitors from Northern Ireland back across the border - and this may change before the weekend.
"But the concept that's being used on the ground - and it's being used across the border as well - is a concept of engage, explain, encourage and enforce."
"An odd time we have to get into the explain concept and encourage concept, not that often.
"But when you try to explain to somebody and you appeal to their better instincts in relation to the risks... that's where most of it is at".
"There is two jurisdictions on this island, but there is one virus.
"And this virus it knows no boundaries - so I think there is a need for a kind of an all-island approach.
"But that's beyond from our side, from our representation of the sergeants and inspectors around the country that we represent.
"That's a Government [issue] for them to sort out and for them to handle.
"But we would love to see that we would have something in place that would give people a little bit more surefootedness on this issue".
He also said checkpoints are expected to be ramped up again for the May bank holiday weekend.
Meanwhile former Tánaiste and Justice Minister Michael McDowell does not believe it is practical to simply tell people crossing the border to go home.
He told Pat Kenny it is difficult to find a solution.
"You can't actually say to somebody on the Northern side of the border 'you may not cross the border because of the COVID regulations'.
"Maybe there's a case for increased scrutiny on the border, but on the other hand what are you going to say at the bridge between Lifford and Strabane?
"Are you going to tell people 'sorry, go home' or 'what are you doing coming across the border?'.
"I don't think that's practical either".