The Oireachtas Committee on Covid-19 Response has been hearing concerns about the disruption to tourism.
In its submission, Fáilte Ireland said the impact of Covid-19 on tourism had been catastrophic and dwarfed all previous crises.
Fáilte Ireland CEO Paul Kelly told the Covid-19 committee that the tourism sector was hit first, hit hardest and will take the longest to recover.
He told politicians that although the sector has had four months of no revenue, the costs have not stopped.
Despite the supports the Government put in place, he said, the industry has incurred over €1 billion in costs.
Mr Kelly said that the 14-day self-isolation requirement effectively closes Ireland to all overseas visitors and that a way must be found to reopen for overseas tourism as soon as public health allows.
Minister for Health Stephen Donnelly said public health officials are concerned a big increase in international travel could see a second wave in Ireland.
Speaking on RTÉ's Morning Ireland, he said he understands that the issue is of great concern to people, who may have already booked holidays or who may be planning a trip abroad, and the National Public Health Emergency is meeting today on the issue.
He said that although airlines have taken a lot of steps to minimise the risk of infection while people are travelling to their destinations, there is no such thing as zero risk.
He said for public health officials the real concern is about people contracting the disease abroad and bringing it back to Ireland.
Cases of Covid-19 in Ireland from international travel was at 2% for the last few months, but has risen to 17% in the last few weeks, he said.
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The minister said the international situation is quite volatile and countries that were doing quite well have seen an increase in Covid-19 cases in the last 14 days, with France reporting 6,000 new cases while 5,000 were reported in Spain and Portugal.
Minister Donnelly said he is looking at the impact of Covid-19 on the health system and other ministers are looking at its impact on education and the economy and it is important to get the reopening of the country right.
He said the situation on reopening Europe's borders is nuanced, with different countries taking different approaches.
Tánaiste and Minister for Enterprise, Trade and Employment Leo Varadkar has said he would like to see a return to international travel as soon as it is safe to do so.
There will be a Cabinet sub-committee meeting on the situation in the next few days, when a decision will be taken.
The Government advice on travel overseas has not changed and Mr Varadkar said all non-essential travel should be avoided at this time.
The Government plans to publish a "green" list of countries by 9 July, indicating where people can travel without a 14-day quarantine.
Mr Varadkar said he hopes a quarantine would not be a long-term requirement because it is very difficult to enforce.
He said there is now a "new normal", but that could all change if the virus returns.
Dr Catherine Motherway, a consultant in intensive care, has said the 14-day quarantine should remain in place.
Speaking on RTÉ's Today with Sarah McInerney, she said most of the early cases of the virus came to Ireland via international travel.
She warned against reopening the country too quickly, pointing out that there a localised outbreaks in some European countries that reopened.
Dr Motherway said she understands the need to get the tourism sector back up and running, but added that a second wave of the virus will serious impede Ireland’s recovery.