The Minister for Transport has said a mandatory quarantine is not possible to enforce for those entering Ireland but stricter control measures are set to be introduced.
Eamon Ryan said those measures will include an electronic register and testing of some travellers.
Speaking on RTÉ's Today with Sarah McInerney, he said the advice remains that in the wider interests of public health it is best to stay in Ireland and not to travel abroad.
He said the Irish approach to Covid-19 is working and the quarantine measures in place are working, but authorities need to remain vigilant and continue to adapt, monitor and review the situation as more people start flying.
He said if the number of cases of Covid-19 rise as a result of international travel "we will have to tighten restrictions".
Minister Ryan said the Government will look to move from a paper to an electronic register for those coming into Ireland and this will allow a follow-up service with text and phone calls to ensure compliance.
He said it is very difficult to get testing that really does work and asymptomatic carriers may not show up in some tests, including temperature tests.
But he said Government wants to introduce a form of testing and see if it can work by targeting travellers from certain countries or those travellers who may have symptoms.
He said the Government and airlines need to be able to work together and that airlines will not get public policy support if they continue with a strategy which contravenes public health.
He said that if people do travel to a country on a green list and it changes status while they are there, they must self-isolate when they return for two weeks.
Minister Ryan said he would prefer to focus public spending on Irish tourism rather than on refunding people who have lost money on international flights and holidays.
He said that government compensation should focus on people who have lost jobs in the Irish tourism industry and to help people to have holidays here.
He said the Government had put in place a refund scheme with travel operators if a package holiday service abroad goes out of business, but this does not cover individually booked flights.
He said most people who are taking flights now had booked "in the last six months", which he said is not appropriate when everyone knew there was a travel risk.
He said the Government is looking at this but his view is that the domestic market needs support.