THE Government has extended its advice for people to avoid all non-essential travel until July 20.
Following a Cabinet meeting on Monday, Taoiseach Micheál Martin said a "green list" of countries which people can travel to will be published on that date.
He also said that the list will be reviewed every two weeks.
He added: "Essentially what we're saying here is countries that have the same disease status as Ireland, or similar to Ireland, will be on that green list, whereby you would be advised that you can travel safely to those countries.
"We will not publish a green list until before July 20 and that list will be reviewed every fortnight because it's changing in relation to experiences in other countries.
"People travelling from countries not on the green list will be required to restrict their movements for 14 days."
Mr Martin said there are fears that international travel will cause a resurgence in coronavirus cases.
Minister for Health Stephen Donnelly also confirmed that the Government will launch the Covid-19 tracker app on Tuesday.
Mr Donnelly said the app could be a "really powerful part of the toolkit" in fighting the disease.
"It allows every single person to play an extra part. It will allow us to get on with contact tracing in a matter of hours," he added.
"It will allow people who have the app to completely control their own data, there will be no centralisation of data, the people themselves can choose if they want to anonymously share with close contacts that they have tested positive, so it's a very, very powerful tool.
"We'll be getting into more of the detail tomorrow and we'll be really encouraging as many people as possible to download and use the app."
Mr Donnelly added that Ireland is already experiencing a "surge" in the number of Covid-19 cases associated with international travel.
"A few months back 2% of new cases were from international travel and it's now 17% of new cases," he added.
"We have largely suppressed the virus in the country thanks to the extraordinary work of every person, every family, and some amazing leadership from the likes of (chief medical officer) Dr (Tony) Holohan and many others."
Minister for Foreign Affairs Simon Coveney told a press conference that the Government made a series of decisions today that need to be "operationalised" over the next two weeks in the State's airports.
This includes the digitised version of the passenger locator form.
"This is to make sure that we can deal with the increased capacity that's going to be demanded of the State in terms of checking up and communicating with people who've come to Ireland from non-green listed countries to ensure that we know where they are and that they understand their responsibilities," Mr Coveney added.
"If you look at the numbers in terms of those travelling now to Irish airports, a week ago there were 1,200 passengers arriving into Dublin Airport. Yesterday it was 4,000.
"So you can see the increased numbers of people who are now travelling to Ireland."
Meanwhile, Professor Kingston Mills said asking people travelling into Ireland from abroad to self-isolate for 14 days was "not working".
Prof Mills, professor of experimental immunology and head of the Centre for the Study of Immunology at Trinity Biomedical Sciences Institute in Dublin, said Ireland has done well in suppressing the spread of coronavirus but allowing unrestricted travel into the country would unravel this.
"We're one of the countries with the lowest levels of the virus in Europe and we're an island. We have a chance to do even better than we have done in terms of completely eliminating the virus and preventing any further surges of the virus," he told RTÉ's Morning Ireland.
"The idea of non-mandatory self-isolation is not really working as I understand there are a significant amount of people not self-isolating or they are not being followed up.
"People are effectively ignoring the advice from Government not to travel because you only have to look at the number of flights going in and out of Dublin to see that."
One more person had died with Covid-19 in Ireland on Sunday.
There has now been a total of 1,741 coronavirus-related deaths in the country, the National Public Health Emergency Team said.