Taoiseach Micheál Martin has faced calls in the Dáil to introduce immediate hotel quarantine.
The Government has also faced criticisms of its handling of new rules and confusing communications in media in the last 24 hours.
Sinn Féin leader Mary Lou McDonald said the Government's "half baked" quarantine plan falls short of what is needed to fight this deadly virus.
The Government must 'drop the half measures' around mandatory quarantine for incoming passengers to Ireland, Sinn Féin leader @MaryLouMcDonald has said | Read more: https://t.co/26sPtPIvtc pic.twitter.com/aKcqOaQZb0
— RTÉ News (@rtenews) February 3, 2021
She said the logic of Minister for Health Stephen Donnelly's comments is that people in quarantine can mix with others in their home.
Ms McDonald said it will be weeks before there is legislation to allow hotels to be used for quarantine.
"We need a mandatory system of quarantine ... and I ask you to drop the half measures," she told the Dáil during Leaders' Questions.
She described the current system of self-isolation in the home as sloppy and loose.
The Taoiseach said the Government has learned that the situation is more perilous because of the virus variant.
Micheál Martin insisted that legislation to allow for mandatory quarantine in hotels will be brought before the Dáil quickly.
Measures have already been taken in relation to international travel, Taoiseach @MichealMartinTD tells the Dáil.
— RTÉ News (@rtenews) February 3, 2021
He says legislation on mandatory quarantine will be introduced 'quickly' | Read more: https://t.co/26sPtPIvtc pic.twitter.com/voDLPKST1f
He said about 50% of the 800 people who travelled into the country yesterday were Irish people returning from holidays.
"Travel has collapsed into the country and it's our intention to keep it at very low levels," he said.
He said there were legal reasons that require careful balancing around the issue of mandatory quarantine in hotels.
The measure must be able to withstand legal challenge, he said.
He repeated that he wants a prolonged suppression of the virus to get the numbers as low as possible.
The co-leader of the Social Democrats told the Taoiseach that the failure to address the issue of travel is the "biggest single failing in relation to the response to Covid".
The Government's failure to address issues around international travel has been the 'biggest single failing in relation to the response to Covid', Social Democrats co-leader @RoisinShortall has said | Read more: https://t.co/26sPtPIvtc pic.twitter.com/qkYo6ym8Nu
— RTÉ News (@rtenews) February 3, 2021
Róisín Shortall said that mandatory hotel quarantine is absolutely essential, to prevent the importation of new cases and variants and said she could not understand why Government will not adopt it.
Ms Shortall said that a zero-Covid approach is the only way to ensure a reopening of society.
She queried the logic of mandatory home quarantining and asked how it could be policed.
The Taoiseach rejected criticism of travel restrictions. He said that people's lives had been curtailed significantly and that it was important to achieve a balance between necessary restrictions and people's liberty.
"How do you police somebody in their bedroom, answer that question, in terms of common sense and practicality of enforcement," the Taoiseach said.
Micheál Martin told Róisín Shortall he believed that she was a late convert to zero-Covid and that she had been "see-sawing" on the issue for some time.
Earlier today, Labour leader Alan Kelly accused the Government of paying lip service to the issue of a mandatory quarantine.
Speaking on RTÉ's Morning Ireland, Mr Kelly said he cannot understand why it will take several more weeks to introduce legislation for mandatory quarantining, and described the situation as "crazy and potentially calamitous".
Mr Kelly said the National Public Health Emergency Team has been calling for quarantine measures to be put in place for several months.
He said an expert group was put together last May to examine the issue and he could not comprehend why primary legislation has not already been drafted.
The Government insisted yesterday evening that it will have legislation ready within weeks.
Under plans announced last week, those arriving here from Brazil and South Africa will spend 14 days in mandatory quarantine.
Other countries could be added to the list at a later stage as part of an effort to keep variants of Covid-19 out of the country.
Those arriving without a negative Covid-19 test are also subject to this rule, but they could leave quarantine should they complete two negative tests within five days of entering the State.
Mr Kelly said he did not believe the Government was treating the issue as a priority and "lip service" is being paid to one of the most important issues facing the country.
Minister for Health Stephen Donnelly said gardaí do not have the legal powers to turn back people travelling out of the country for non-essential reasons.
Speaking on Newstalk radio, he said it is not okay for people to assume that they can simply travel and will just pay a fine, adding "I can assure you that Government will look at that".
Mr Donnelly said that 813 people arrived into Dublin airport yesterday.
He said people who are arriving into Ireland must adhere to the relevant quarantine period and in most cases people need to stay in their house.
He said regulations will be signed either today or tomorrow, which will bring in mandatory home quarantine.
Minister Donnelly said that what is legally possible is to tell people they need to stay at home but the law does not extend inside the house and tell them what room to stay in.
He said in cases where people are living with others but who have travelled alone, they should self-isolate as
they may potentially put other people at risk.
However, he said, if it is a family situation where people have been mixing together anyway, the rule is to quarantine at home, but people do not have to self-isolate in separate rooms.
Minister for Foreign Affairs Simon Coveney said the Government recognises the need to add further restrictions involving mandatory quarantine - some of which will have to happen in State-run facilities.
He said he hopes the Dáil will co-operate so that necessary legislation can be passed quickly.
Mr Coveney said his understanding is that quarantining at home means the person restricts their movements to their home, while self-isolation requires a person to separate themselves from the rest of the household.
Meanwhile, People Before Profit's Richard Boyd Barrett accused the Government of "playing with fire" and of balancing half measures at ports and airports against half measures on non-essential travel.
He said garda spot checks on whether people arriving into Ireland are quarantining at home, "are random and will not cut it".
He said "the idea that you can police people in their homes is nonsensical and I'm sure even the guards will acknowledge that and it has to be done at ports and airports in an effective way.
"That will essentially end non-essential travel and then require quarantine for those who are essential and we need to strictly define what essential is."
He said we need decisive measures to make sure non-essential travel does not happen.
He said we can break the country into zones, as in Australia, that don't require erecting a hard border, but are simply about enforcing the 5km measures for people not moving for non-essential reasons until we have driven down community transmission.
Additional reporting Tommy Meskill
