The new Health Minister says there is no commitment yet to when a list of countries Irish people can travel to without quarantining on their return will be published.
The previous government pledged to producing a "green list" by next month.
Last Thursday, the former government announced that foreign travel to certain countries from July 9 has been approved.
Air bridges will be established between countries with similarly low infection rates from that date, enabling people to travel without undergoing quarantine.
“The risk of it being imported into the country is no higher than from one county to another," Leo Varadkar said last week.
The Chief Medical Officer has raised concerns over the return of international travel, saying it risks a second wave of the coronavirus here.
Stephen Donnelly, who was appointed Health Minister yesterday, says the list will be kept under review.
He said: “Two weeks ago, you might have looked at Portugal, and said Portugal has a very low case rate of Covid.
“It has been consistently low and so that is an obvious country that you would put on a green list.
“But just in the last few days, Portugal has seen a big surge.
“There are countries like Sweden and…the island of Britain where the rates are significantly higher than ours.
“So there’s a lot of detail that would need to be worked through on this.”
Yesterday, CMO Dr Tony Holohan advised people that this year, holidays should be about "staycations”.
Writing on Twitter as the country prepares to move into Phase Three of reopening society, he said: "What worries me most now is travel from overseas and I fear many planning foreign trips.
"2020 is a year for a staycation. Stay in Ireland, spend locally and follow public health advice."