Couples from Northern Ireland jetting out of Dublin for a holiday are set to be hit with a €4,200 - around £3,700 - on the spot fine.
Fines in the Republic for travelling abroad for a non-essential reason are set to increase to €2,000 (£1,788).
People from Northern Ireland also face a €100 (£88) for entering the Republic unnecessarily.
Taoiseach Micheál Martin has asked Health Minister Stephen Donnelly to sign off on regulations which will increase the existing €500 (£440) fine to €2,000 (£1,788) as soon as possible.
The move is part of a number of measures aimed at clamping down on foreign travel as the Irish Government battles to control the third wave of Covid-19.
Mandatory home quarantining is already introduced under law for anyone arriving in the Republic. Legislation for hotel quarantining is expected before cabinet next week, the Taoiseach told the Dáil.
The new €2,000 fine for breaching restrictions for travelling abroad will be a major deterrent for people thinking of going on holidays. The €500 fine which was only recently introduced was not seen as enough of a deterrent to stop people travelling abroad.
Gardai have set up roadside checks near Dublin Airport to issue fines to people leaving Ireland for non-essential reasons.
A total of 13,606 passengers arrived into Dublin in the week ending last Friday, it has emerged. Of these 8,218 were Irish residents and the remainder, amounting to 5,388 were non-residents, the Government disclosed.
Of the 8,218 Irish residents, more than two-thirds - 5,241 people - stated that they were returning from a holiday or a visit abroad. These 5,241 passengers account for 39.7% of all passenger arrivals into Dublin Airport, and 63.8% of all Irish resident arrivals into Dublin Airport.
Non-essential overseas travel is a breach of level 5 regulations and "it is important that everyone understands and respects that," a spokeswoman said.
"About 60% of those travelling are returned Irish holidaymakers. There is a sense that €500 is not a sufficient disincentive to travel abroad. That will be increased," Mr Martin told the Dáíl.
"The Government is considering increasing that to €2,000 to act as a significant deterrent to people travelling because all non-essential travelling should be avoided. It is also the intention to bring forward legislation for approval to Cabinet next Tuesday to deal with mandatory quarantining."
Overall passenger numbers are a tiny fraction of normal levels - below 3% for this time of year, with the 13,600 in the last week comparing with over 230,000 in the week in 2020, before restrictions came into force.