Taoiseach (Irish PM) Micheál Martin has expressed concerns about travellers coming into the Republic of Ireland from Great Britain.
It comes as quarantine rules have ended for people arriving in the UK from more than 50 countries.
Irish authorities require anyone coming into the Republic of Ireland, apart from from Northern Ireland, to self-isolate for 14 days.
That advice remains in place until 20 July.
In his first interview with BBC Northern Ireland’s Sunday Politics since becoming taoiseach last month, Mr Martin said he believed travel off the island of Ireland at this time was “problematic”.
“We have issues with the UK, in terms of Leicester where it closed down recently,” he said.
Irish government remains ‘cautious’
“It’s not just the UK; it’s international travel in general. Our current advice is against international travel off the island of Ireland because we believe it’s problematic and our public health people are saying that to us.”
Mr Martin said he hoped the Irish government would publish a “green list” on 20 July that would indicate which countries could be safe for travellers, with a lower risk of the virus spreading.
He added that the government remained very “cautious” about international travel.
On Thursday, public health authorities in the Republic of Ireland said 15 of 23 new confirmed cases of the virus were “directly or indirectly related to travel”.
Prof Philip Nolan of the Irish National Public Health Emergency Team said officials were seeing an increase in the number of reported cases over the past two weeks in the Republic of Ireland.
Mr Martin said the island of Ireland had done well in terms of containing the virus, and pointed to the memorandum of understanding signed by ministers and officials in both jurisdictions in April.
“It is a very good, practical illustration of what we are trying to do,” he added.
Mr Martin is expected to visit Stormont next week and meet the first and deputy first ministers about the ongoing response to coronavirus, after a planned trip on Thursday was postponed.
You can watch the interview in full on Sunday Politics with Mark Carruthers on BBC One NI and BBC iPlayer on Sunday 12 July at 10:15 BST.