The Health Minister says the Government will consider giving additional powers to the Gardaí, if issuing fines to holidaymakers doesn't discourage travel.
Anyone caught traveling abroad for a non-essential reason can now be fined 500 euro.
However Gardaí currently do not have the power to arrest non-essential travellers.
813 people arrived into Dublin Airport yesterday.
Minister Stephen Donnelly says if fines aren't enough they will reexamine the issue.