The Government has agreed to add 15 countries to a 'green list' where the travel advice will be to take normal precautions.
People returning from these countries will not have to restrict their movements for a 14-day period.
The 15 countries are: Malta, Finland, Norway, Italy, Hungary, Estonia, Latvia, Lithuania, Cyprus, Slovakia, Greece, Greenland, Gibraltar, Monaco and San Marino.
The general advice to avoid non-essential travel will apply to all other countries. People who arrive in Ireland from countries not on the green list will still have to restrict their movements.
The list, which was agreed following a meeting of the Cabinet at Dublin Castle, will be reviewed every fortnight.
The National Public Health Emergency Team advice remains against all non-essential foreign travel, regardless of whether a country is on the green list or not.
Earlier, Tánaiste Leo Varadkar had questioned whether the green list should be published at all, if the NPHET advice remains in place.
There were differing views ahead of the Cabinet discussion on the issue, with one Cabinet source saying that a "substantial discussion" is needed before a decision can be made.
A spokesperson for Mr Varadkar said he believes it is wrong to send out mixed messages about international travel.
He believes there should be a green list, as was previously agreed by the Government.
"But if the travel advice for countries on the green list isn't different to advice for other countries, then we would be better off not having a green list at all," he said.
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Speaking as he arrived at Dublin Castle before the meeting, Minister for Further and Higher Education Simon Harris said Fianna Fáil and Fine Gael are not at odds on the plan.
He was echoing comments made by Minister for Housing Darragh O'Brien, who said there is "absolutely no division at Cabinet" on the publication of the list.
Speaking on RTÉ's News at One, Mr O'Brien said the priority of the Government is on public health and the advice remains to avoid non-essential travel abroad.
Green list must not be seen as a green light for holidays, says medics
Acting Chief Medical Officer Dr Ronan Glynn and other senior medics have stressed the green list should only be for essential travel and must not be seen as a green light for holidays.
Irish College of General Practitioners President Dr Mary Favier also said that all non-essential travel needs to be limited as much as possible, even with a green list.
She said: "A green list is going to be very limited by necessity, while it will be safe to travel I think there are limitations to that safety, because if you think about it, you may be going to an area that has a lower infection rate than us, [but] you can't control who goes there.
"They may be coming from countries that have a much higher replication rate than us, they may even be coming from the United States, the United Kingdom. We would still be recommending if you don't need to go really think twice about whether you should go."
Dublin Airport Authority spokesperson Siobhán O'Donnell said Dublin Airport had been preparing for any uptake in passenger numbers, including Covid-19 information signs, compulsory mask-wearing in terminal buildings, only allowing intending passengers inside terminal buildings, and making hygiene sprays and hand gels available.
She said while health issues are "to the front of our mind", airport officials are also aware that instead of being "right in the middle of our peak summer season when we'd have around about 115,000 passengers, you look here now and there's a handful, a trickle.
"We were building on a record year of almost 33 million passengers last year, and the outlook was really good.
"January was a good month, February was a good month, and then we all know what happened after that.
"It looks like it's going to take a long, long time for any kind of normal to return back. It's hugely concerning."
Additional reporting: Mary Regan, Fiachra Ó Cionnaith