Taoiseach Micheál Martin has said the Government will take a cautious approach to international travel and non-essential travel is not advised until at least 20 July.
On that date, a so-called "green list" of countries with similar levels of the virus to Ireland will be published. That will be followed by an easing of travel restrictions between those countries and Ireland.
Mr Martin said Covid-19 remains volatile judging by what is happening in other countries and Ireland needs to keep it suppressed.
He said that the Government's priorities include the reopening of schools as fully as possible in September along with increasing capacity in the health service to provide non-Covid treatments, and it will not do anything to jeopardise these aims.
Mr Martin said last weekend was a challenging one and rules around pubs must be strictly applied.
He said the Government was very worried about what had happened and nothing can be guaranteed when it comes to the reopening of all pubs planned for 20 July. Countries on the so-called "green list" would have a disease level similar to Ireland, the Taoiseach added.
The list will be reviewed every fortnight.