The Government is seeking to increase fines for non-essential international travel from €500 to €2,000.
Speaking in the Dáil, Taoiseach Micheál Martin said that around 60% of international travellers arriving into Ireland are returning Irish holiday makers.
He told Labour's Duncan Smith that "there is a sense that €500 is not a sufficient disincentive to travel abroad".
Legislation will be brought forward for approval by Cabinet next Tuesday to deal with mandatory quarantine.
Minister for Transport Eamon Ryan said public health advice will come later this afternoon on which countries should be added to the mandatory quarantine list.
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Labour leader Alan Kelly said mandatory hotel quarantine needs to be introduced immediately.
Speaking on RTÉ's News at One, he said it is not good enough that it will be a number of weeks for the legislation that is being brought in to become operational.
Mr Kelly said that "we've locked up our people three times to stay within 5km of their homes, the choice into the future is do we continue to do that or do we quarantine people coming in".
Earlier, the Assistant Secretary General at Department of the Taoiseach said the number of Irish people returning from holidays "is a very concerning statistic".
Speaking at a news briefing, Liz Canavan said "while overall passenger numbers are a tiny fraction of normal levels, below 3% for this time of year, over half of the passengers arriving into the country are Irish residents and two thirds of those are returning from holidays".
She said while people would all love and need a holiday "now is not the time to travel", and urged people to stay at home unless they have to travel for a specific essential purpose.
Ms Canavan said that anyone who arrives into Ireland without a negative PCR test is obliged to take one on arrival.
She said regulations have also been amended so that the same rules and obligations when it comes to testing and quarantine apply to those into Ireland from overseas via Northern Ireland.
Non-essential overseas travel is a breach of Level 5 restrictions, says Liz Canavan. The fixed penalty for this has been increased to €500. Over half of the passengers arriving are Irish residents, and two-thirds of those are returning from holiday. | https://t.co/HpctZNic2c pic.twitter.com/2qc0uZ6igt— RTÉ News (@rtenews) February 10, 2021