The Labour Party has said the public want more stringent measures around mandatory quarantine for travellers coming into Ireland.
It comes after a Labour motion to extend mandatory quarantine to all non-essential travel was defeated on Thursday.
New mandatory hotel quarantine laws passed in the Dáil by 103 votes to 10 - but this now has to go through the Seanad before taking effect.
Labour's education spokesperson Aodhán Ó Ríordáin told Newstalk Breakfast he believes there is an appetite for tougher measures.
"A vote was taken and Government are going to do what they said they would do.
"They've a list of 20 countries, but the UK have 33 countries - Government have said they want to add to their list.
"I believe that there is a level of support for us taking this very serious[ly] for a specific period of time.
"The virus moves from country to country - the idea that we'd have 20 countries and that would be it doesn't make much sense to us.
"We wanted to be much more comprehensive about a strategy of mandatory quarantine."
Deputy Ó Ríordáin said he hopes the Government is right on this.
"Hopefully the Government are right, maybe we are wrong - either way we want to see the stats going down, but they are stubbornly high."
On the re-opening of schools next week, he said this has to be viewed as part of the overall plan.
"We are going to open up schools - which is something that we support - we're talking about opening up other elements of the economy, including constriction.
"If we do that in tandem with a policy of restricting inwards travel to 20 countries we're not convinced it's going to work, we hope to be wrong.
"But what we want to see is not taking these different decisions and divorcing them from each other.
"The re-opening of schools is completely part of an overall strategy, and what we don't want to see is that we have to close schools again because the strategy doesn't work.
"We want it to be more comprehensive: 20 countries on a list is just not going to cut it".