Sinn Féin has said the number of countries from which arrivals have to quarantine in a hotel for 12 days must be expanded in line with public health advice.
The party's spokesperson on health, David Cullinane, said there are very high rates across many countries "with variants of concern and widespread transmission driving up cases across Europe and North America".
The Government added 26 states to the list last night. But EU countries were not included after resistance from the Minister for Foreign Affairs Simon Coveney.
Minister for Health Stephen Donnelly still strongly supports the public health advice to add countries including France, Germany and Italy, and the issue will be revisited early next week.
Mr Cullinane accused Fine Gael of "cherry picking" public health advice and "going half the distance" on measures to reduce the spread of Covid-19.
"The public health advice must be implemented in full. Fine Gael are unnecessarily causing division on this issue and holding up the expansion of hotel quarantine," he said.
"It makes no sense that they would prevent a robust quarantine system to protect against important dangerous variants and more cases when the public have sacrificed so much to get to this point.
He said the failure to implement the advice will "see us all locked down for longer" and that importation of the South African variant "could have a serious impact on our vaccine programme".
Meanwhile, Irish residents arriving into the country who have an alternative place to quarantine rather than a hotel should be able to do so if proper inspections are put in place, Fianna Fáil MEP Billy Kelleher has said.
Speaking on RTÉ's Today with Claire Byrne, Mr Kelleher said countries that have a high prevalence of the Covid-19 variant first detected in South Africa pose a risk.
When countries are being added to the list it should be based on risk to public health as opposed to the impact it may have on travel issues or fundamental freedoms, he said.
While we are rolling out the vaccination programme, we cannot heighten risk, Mr Kelleher said. There is always a balance to be struck, but it must be struck "firmly in favour of public health" in the short term.
He also said that if an Irish resident is coming into the country and can identify a place other than a hotel, you "should be able to probably quarantine at home" with proper inspection systems put in place.
"Otherwise our hotel system will not have the capacity in terms of quarantining," Mr Kelleher said.
"So that is an issue, because between France, Germany and Italy alone there must be 50,000 to 60,000 people at least - Irish citizens - living in those countries. If any percentage of them wants to come home for any reasons it could overwhelm the system."
The Ireland South MEP said people coming here from Europe are doing so because "it is easy" as there is no obligatory hotel quarantine system and home quarantining is not being enforced in terms of inspections.
Variants need to be kept out, he said, until we get to a stage where we have potential herd immunity across the population.
He said the South African variant is virulent in France at the moment and the rest of Europe is heading for a "huge third wave".
"If we are to use hotels we should use them in a way that discourages people from coming in the short term, but if they do come, they have to quarantine either in a hotel or if there's some system being able to provide alternative accommodation that is inspected, then that's something that should be looked at.
"But we can't do nothing at the moment, it could just risk all that we have achieved."
Senator Michael McDowell said the argument about whether EU law somehow prevents us having travel restrictions for anyone arriving from an EU country is "a bit overblown".
If there is evidence that a variant could enter Ireland from an EU member state if we do not take precautions, he does not see a problem with imposing restrictions "as long as it's necessary, it's proportionate and it's non discriminatory".
Speaking on RTÉ's Today with Claire Byrne, the former Justice Minister said what he meant by "non discriminatory" is there cannot be a situation where an Irish person arriving here from France does not have to quarantine in a hotel but a French person arriving here from France does".
On the same programme, People Before Profit TD Paul Murphy described the situation as "a joke" and said public health advice is being trumped by geopolitics.
It is about the theatre of pretending to do something without actually doing it, he said, adding that 10,000 travellers are coming here every week and only a "tiny proportion" are required to do mandatory hotel quarantine.
"Which means that Covid is still coming in because there's no enforcement of the fact that people are meant to be quarantining at home," Mr Murphy said.
"It is almost pointless what the Government is doing, but they get to say 'oh we're having mandatory quarantine'. If you look through the list of states, it's not going to add much pressure to the hotels because nobody comes in from these states."
It is not grounded in public health advice, he said, and "does not make sense".
Sinn Féin TD for Mayo, Rose Conway-Walsh, said voluntary quarantining at home "has not worked".
Speaking on the same programme, she said the Government is "choosing to ignore" public health advice on hotel quarantine.
Nobody wants a situation where people are being prevented from coming into the country, she said, but it is necessary on a temporary basis.
"Three people tested positive that came in last week," she said.
"If they had the variant in France that cannot be picked up by a PCR test and that spread here, what do we do? How do we manage that?"