People flying to Ireland from abroad are still bringing Covid-19 into the country, with 235 infections confirmed among air travellers since May 1.
Overall, 582 people who picked up the virus abroad have been diagnosed since the crisis began. Many of them were on holiday in February during the early phase of the spread.
Despite hardly anyone flying since the Government advised against non-essential travel, a steady number of airline passengers are continuing to be diagnosed.
It comes as more countries in Europe are opening their borders, with Spain ready to welcome tourists from most European countries from next Sunday and airlines gearing up to resume flights to the continent next month.
Meanwhile, the Department of Health announced another three more deaths from the virus in the Republic yesterday, bringing the total to 1,709.
Fourteen more people tested positive.
It means that 25,334 have been diagnosed since Covid-19 hit these shores.
The downward trend comes as the National Public Health Emergency Team (Nphet) is set to meet to decide on what restrictions should be relaxed for the next phase of exiting lockdown on June 29.
It may also signal its views on whether the two-week quarantine guideline for all people flying into the country should be fully removed or maybe modified.
"As of midnight on Monday, June 14, a total of 386,572 tests have been carried out," Chief Medical Officer Dr Tony Holohan said. "Over the past week, 18,758 tests were carried out and 146 tests were positive.
"That gives a positivity rate of 0.8pc."
A study in the Lancet medical journal has said that in the absence of a vaccine or highly effective treatments for Covid-19, combining isolation and intensive contact tracing with physical distancing measures - such as limits on daily social or workplace contacts - might be the most effective and efficient way to achieve and maintain epidemic control.
The study, which was led by the London School of Hygiene and Tropical Medicine, looked at data on more than 40,000 individuals.