Gardaí say anyone visiting the state has to abide by the laws of the Republic.
It is after reports that anyone down here on a day trip from the North would not be affected by the coronavirus rules.
Reports say the restrictions on movement south of the border due to coronavirus do not apply to people on day trips from Northern Ireland.
It was reported there was a gap in the law that would mean the regulations on travel do not affect them and they can't be arrested.
But in a statement, gardaí are urging everyone resident or visiting this State to stick to the public health guidelines to protect themselves and others from Covid-19.
The force says it remains the case that anyone visiting the State even temporarily, is amenable to such criminal laws of the country during their time here.
It says the detail of a particular piece of legislation is a matter for the relevant Department.