Micheál Martin's proposal comes amid reports passengers are currently paying the fine and carrying on with their international journey.
Taoiseach Micheál Martin has proposed for new regulations to be introduced which would increase the fine for non-essential international travel to €2,000.
As it stands, those caught breaching the current regulations are obliged to pay a €500 fine.
However, reports suggest that a number of travellers are currently paying the fine, and then continuing on with their journey, leading Martin to propose a more prohibitive punishment.
Martin confirmed the plan to the Dáil on Wednesday afternoon.
Speaking in the Dáil, he said that around 60% of international travellers arriving into Ireland are returning Irish holidaymakers.
Martin told Labour's Duncan Smith that "there is a sense that €500 is not a sufficient disincentive to travel abroad" and said that the increased fine would aim to "act as a significant deterrent" to non-essential travel.
The Government is now also considering mandatory hotel quarantine for people coming into the country for non-essential reasons from holiday destinations.
Martin said that legislation will be brought forward for approval by Cabinet next Tuesday to deal with mandatory quarantine.
Martin's proposal comes after it emerged earlier on Wednesday that 13,600 people arrived into Dublin Airport from overseas last week.
