Minister for Health Simon Harris has said it is "not looking good" for foreign travel this year.
He said the advice at the moment was not to leave the island of Ireland and it was looking highly unlikely that people would be able to travel abroad for holidays later in the year.
He pointed out that anyone travelling into Ireland now has to self-isolate for 14 days and said other European countries also have their own restrictions in place.
Passengers travelling into Ireland are now asked to complete a Public Health Passenger Locator form, showing their contact details and the address at which they will self-isolate.
The minister said the Taoiseach had asked a number of ministers to consider, with the Attorney General, if this needed to be underpinned by regulations and he said a decision on this was due in the coming weeks.
He said at the moment very few people were travelling into Ireland but that could change in the months ahead.
The minister welcomed the fact that the number of confirmed cases of Covid-19 in ICU has fallen to below 100 for the first time since the end of March.
He said this offered some encouragement although he noted that this figure represented 99 people who were very sick and whose families were very worried.
The number of people in ICU is a figure health authorities have to watch very carefully over the coming weeks, he added.
Minister Harris said as of yesterday afternoon, 169,377 tests for Covid-19 had been completed. He said Ireland was doing more testing per head of population than many other countries and was ambitious to do more. He praised the work of the Health Service Executive who had no testing infrastructure a couple of months ago.
The minister said yesterday was a significant milestone in our collective national effort. There were now two weeks, he said, to make the virus as weak as possible. He said he was conscious of how difficult it was for older people to cocoon and he said the Government would monitor how cocooning could "evolve" as appropriate.
In relation to complaints from vintners that restaurants and cafes will be able to open in an earlier phase than pubs, he said the Government was willing to meet any businesses who could put forward suggestions as to how they could reopen safely.
The minister reiterated that the move from each phase of the reopening plan was not guaranteed.
He said it was entirely dependent on the behaviour of the virus and how we all embraced and followed public health advice.
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The plan was a living, breathing document which aimed to offer people a degree of certainty, he explained.
Minister Harris said he was very conscious of the risk of a second wave of the virus and there was a chance this could happen. This was why hospitals had to have spare capacity, he said. He would be receiving public health advice and reporting to Cabinet every three weeks in relation to the situation.