The Taoiseach Micheál Martin has confirmed that Government advice against all non-essential travel will remain in place until 20 July.
He was speaking at a post-cabinet media briefing this afternoon.
The Taoiseach said international travel is not advised and should be avoided.
He said a "Green list" of countries to which people can travel to and from will be published on 20 July.
He said there is no change on travel to and from Northern Ireland.
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.
Mr Martin said sectoral protocols will be published by the Department of Transport, and a list of exemptions will continue to apply to facilitate the transit of essential workers.
He said the current paper based passenger locator form will be replaced by an electronic system to capture passenger data directly from airlines and ferries.
The regulations underpinning passenger locator form will extend until 20 July.
The Taoiseach said "we know from reports seen at the weekend of an internationally volatile situation", and referenced Spain and the UK.
He said the situations in these countries are "informing" the Government's view, "as we see second waves emerging", he added.
"We have to make sure that in this country that the number of cases remains low, that community transmission remains low and that the R rate is kept below 1."
Micheál Martin said that two key objectives from now until the end of the summer and beyond is to ensure that schools can reopen fully at the end of August, and that non-Covid-19 healthcare can be continued.
"We need to deal with non-Covid illnesses, diseases and screening programmes. It is essential where we not have capacity in our hospital system.
"Critical care beds in use have come down to low figures. We don't want any spike in cases that may undermine this," he said.
Foreign Affairs and Defence Minister Simon Coveney said public health officials believe that foreign travel is the number one risk for a second wave of the disease.
He said "what we are going to do between now and 20 July is to put a green list together of countries at a similar risk or less than Ireland".
He said people travelling to or from those countries will not be asked to self-quarantine but for all other countries they will.
Yesterday he said, there were 4,000 arrivals into Dublin airport and "we need to understand where all those people are going".
The Minister for Health Stephen Donnelly has said the public health advice is against all non-essential overseas travel.
He said there are a lot of people who would like to see loved ones abroad but public health officials are very worried about the potential for a second surge brought about by an upswing in foreign travel.
He said what is of most concern is that people do not travel to countries not on the green list, when it is published.
He said a Covid tracker app will be launched tomorrow that will be a "really powerful part" in tracking the disease. He said the app will allow people to control their own data, saying it's a very powerful tool and they encourage as many people as possible to download it.