Fines for non-essential overseas travel are set to increase to €2,000 the Taoiseach has said.
Micheál Martin said that around two-thirds of people arriving into Ireland from abroad were returning Irish holidaymakers.
He told the Dail he had asked Health Minister Stephen Donnelly to sign off on the four-fold increase from €500 to €2,000.
"There is a sense that €500 is not a sufficient disincentive to travel abroad," Mr Martin said.
Mr Martin said he intends to bring legislation to Cabinet on Tuesday to sign off on the increased fines and deal with mandatory quarantining.
The move is part of a number of Government measures aimed at reducing non-essential travel and protecting citizens from the risk of new variants of Covid-19 entering the country.
People are already required under law to quarantine in their homes for 14 days on their arrival into Ireland.
If they fail to do so, they can be fined up to €2,500 or get a prison sentence of up to six months or both.
Passengers who have not arrived from Brazil or South Africa can exit quarantine after five days if they take a PCR test and receive a negative result.
Transport Minister Eamon Ryan said that the fines were being increased to €2,000 following consultation with public health officials and that if there was any evidence that it was "not proving a restraint or restriction" the Government would consider increasing it again.
The fixed penalty fine for breaching the Level 5 travel restrictions on overseas travel has already been increased from €100 to €500.
Mr Ryan also said more countries would be added to the mandatory hotel quarantining list and that "urgent work" was under way to establish a mandatory quarantine facility for passengers arriving from high-risk locations associated with new variants.
Brazil and South Africa are currently on the Government's hotel quarantining list, although the system has yet to be set up.