An infectious diseases expert says travel should continue to be restricted to England and the US next month.
The government's decided to allow foreign travel to resume between some countries from July 9th.
The Taoiseach says a 'green list' of states will be put together - and these would be exempt from the 14-day quarantine rule.
People will also be allowed travel anywhere in Ireland from Monday.
Professor Sam McConkey, from the RCSI, says international travel should be re-introduced very cautiously.
During last night's announcement, the government also confirmed face coverings are to be mandatory on public transport.
Some self-employed people are to be given grants of up to 1,000 euro to help restart their businesses.
Social Protection Minister Regina Doherty also says the school meals programme will continue during the summer holidays
