Chief Medical Officer Dr Tony Holohan says he is 'beyond nervous' about any increase in foreign travel.
He was speaking after the Government yesterday announced plans to introduce 'air bridges' between Ireland and countries which have the virus under control.
It means travel will be allowed between Ireland and certain countries from July 9th.
However, no details have yet been provided on which countries would be involved - with officials saying the list won't be confirmed for two weeks.
Dr Holohan today said there are "many countries" - including in Europe - which wouldn't make the cut today.
He explained officials signing off on travel to any given country would need to 'trust the information' provided by that country, and then that the data would need to show that transmission levels of the virus were low.
He noted: "There would be a lot of countries in Europe not on that list.
"It's quite impossible, given that today is the 26th of June, to say what countries would be on that list on the 9th July.
"If we constructed such a list a week ago, some of those countries would not be on that list today - I accept that creates a challenge for people in terms of plans and forward-booking.
"Our public health advice remains the same - we are recommending avoidance of all non-essential travel from this country... we're asking [people] to avoid planning travel at this time".
He said authorities are also asking tourists from abroad to avoid coming here for now.