Sinn Féin TD Pearse Doherty has argued the introduction of mandatory quarantine is happening too late and described a "half-baked attempt" from Government in addressing this issue.
Speaking on RTÉ's Saturday with Katie Hannon, Mr Doherty said it is extremely frustrating for people and that there should have been a travel ban implemented immediately by Government when it knew of the new strain identified in Brazil.
Mr Doherty, who is Sinn Féin’s finance spokesperson, said the fear is that with the variant now detected in Ireland, what if there are people who have not come forward who might be infected with it.
He said his party argued, because there was no mandatory quarantine, that there should have been a travel ban as soon as the Government had heard about the Brazilian variant.
Green Party leader and Minister for Transport Eamon Ryan, meanwhile, said he believes mandatory hotel quarantine will be "up and running" in a week or two.
Speaking on the same programme, Mr Ryan said it will be introduced in the Dáil next week and it needs debate there and in the Seanad because of civil liberties and other issues.
"It is not insignificant legislation," he said.
He predicted that very quickly, "in a short week or two", it will be through the Dáil and the Seanad and then in operation.
In the meantime, he said, the gardaí are checking to ensure people who are meant to be quarantining on their return from abroad are complying with this measure.
He said accommodation for hotel quarantine has not been secured yet, stating the legislation has to be the first thing.
"At the same time the contract arrangements will be put in place," Mr Ryan said.
Currently he said anyone travelling into Ireland from abroad has to quarantine and those coming from 20 countries listed by the Chief Medical Officer have to mandatory quarantine for a full 14 days.
He said there is the right sense of urgency to respond to this issue of travel and that it is coordinated with the European Centre for Disease Control and the UK because of the border on this island.
"In managing that, to follow a two-island strategy is the best and safest way."