Coronavirus: Ireland's travel advice extended to 20 July
Official government advice against all non-essential travel from Ireland is to remain in place until 20 July.
A requirement for people arriving in the Republic of Ireland from overseas to quarantine for 14 days was to be lifted on Thursday.
The Irish government had planned to publish a "green" list of countries.
However, concern about surges of the virus in other countries prompted health advice that those restrictions should remain in place.
A list of "green countries" will now be published on 20 July.
Speaking at a post-cabinet media briefing, Taoiseach (Irish prime minister) Micheál Martin said that there will be no changes on travel to and from Northern Ireland.
Mr Martin said Ireland will "develop a methodology" in terms of assessing which countries might be on a green list, in terms of travelling to and from Ireland.
He said countries on this list would have "the same disease status, or similar disease status to Ireland".
The "green list" will be reviewed every fortnight.
Mr Martin said the Department of Health would examine proposals for testing at points of entry into the country.
He said there will likely be significantly "heightened visibility" of public health officials at airports, border controls and ports.
The country's health minister said that in the last few months, about 2% of new cases came from international travel and that had "gone up to 17% in the last week".
Stephen Donnelly was talking about the issue of so-called travel air bridges.
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However, Mr Donnelly said public health experts have "a real concern" about the possibility of a second wave of the virus in the Republic of Ireland if there is an increase in foreign travel.
"The international situation was always quite volatile but has become increasingly volatile in the last few weeks," he added.
It comes as it emerged that cluster cases in private households in the Republic of Ireland have increased.
In Micheál Martin's first week as taoiseach, ministers will also review whether public health guidelines are being breached in pubs and other premises one week after they reopen.
On Sunday, the Irish Department of Health said there were no further deaths of people who had previously been diagnosed with Covid-19.
The overall death toll is 1,741.
The department also said there was an additional 18 confirmed cases of the coronavirus.