The Government has removed five destinations from its travel green list.
Malta, Cyprus, Gibraltar, San Marino and Monaco have now been dropped.
Last month, the Government published its green list, whereby people returning from those areas do not have to restrict their movements for a 14-day period.
Finland, Norway, Italy, Hungary, Estonia, Latvia, Lithuania, Slovakia, Greece and Greenland remain on the list.
People who arrive in to Ireland from countries not on the green list have to restrict their movements.
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.
Tánaiste Leo Varadkar has said the Covid-19 pandemic is "blazing" around the world and he said the number of new cases is rising again in Europe.
Speaking at a post-Cabinet briefing, he said Ireland was in a relatively good position and added that the Government wants to keep it that way and not risk schools reopening in a few weeks' time.
Minister for Health Stephen Donnelly has said 14 of the 15 countries and territories on the green list have seen significant increases in the virus in the last two weeks since the list was created.
He said the green list is being updated and narrowed due to what is going on in some of those countries.
The minister said that ten days ago the five day average for Ireland was 20 new cases per day and that has now risen to 53 new cases per day.
Mr Donnelly said that it would not take much for new clusters to spill more into community transmission and he said due to this the Government was not moving to phase four.
He also said that the Government is working with officials in Northern Ireland to see how they can share information for the passenger locator forms tightening up an all-Ireland approach.
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The co-leader of the Social Democrats, Róisín Shortall said she was "surprise" that there were no measures announced "to address the fact that 90% of people travelling into Ireland are from non-green list countries".
Deputy Shortall said: "Despite the Minister for Health floating the unworkable idea of random testing of visitors over the weekend, there was no mention this evening of any plan to put adequate controls in place at our ports and airports."
She said the tracing of passengers arriving into Ireland "has been a shambles, with only 7% receiving calls and half of these not being answered".
She said: "Travel continues to be this Government's main weakness in its response to the Covid-19 crisis."