The number of reported cases of Covid-19 in Ireland has begun to increase, the chief medical officer warned.
Some new clusters have been established.
The country had driven down the number of infections in recent weeks.
Dr Tony Holohan said: "We are starting to see a worrying trend, with the number of reported cases increasing, and some new clusters."
There were no new deaths reported to the Health Protection Surveillance Centre on Monday. There has now been 1,735 Covid-19 related deaths.
As of midnight Sunday June 28, public health chiefs have been notified of 24 confirmed cases, bringing the total to 25,462.
At least six new Covid-19 cases in Ireland were associated with international travel, health chiefs warned on Monday.
The chief medical officer has said he is deeply worried at the prospect of greater foreign travel associated with easing restrictions next month.
Irish ministers had been intending to put in place air bridges with countries with low coronavirus infection rates by July 9 allowing them to bypass quarantine in an effort to boost tourism.
Dr Holohan has expressed concern at the plan and said many of the most popular European holiday spots did not have low enough disease rates to encourage travel to there.
Dr Ronan Glynn, deputy chief medical Officer, said: "Today we are reporting at least six cases associated with international travel.
"Many countries around the world are still experiencing high and increasing levels of this disease.
"Last week, there were over 1.1 million cases reported and there have now been over 10 million cases reported globally to date.
"The risk of imported cases remains high. It's important that we continue to avoid all unnecessary travel at this time."
Dr Holohan said the number of people who were likely to travel from Ireland for non-essential trips then return was greater than the total of tourists from outside the country coming in.
He said a cluster of infection in the north west of the country was associated with travel from Iraq.
Dr Siobhan Kennelly, a Health Service Executive official specialising in the elderly, said: "Many restrictions have now been lifted and people are getting out more, including those who are over 70 or medically vulnerable.
"Socialising is important for your mental and physical wellbeing, but it is important that you are safe while doing so.
"Wear a face covering, know the symptoms of Covid-19 and contact your GP straight away if you feel unwell."
Research conducted on behalf of the Department of Health showed a further increase in the proportion of people who self-reported to be wearing face coverings, now at 45%.
The level of worry was increasing with 49% believing the worst is behind us and 23% thinking it lies ahead, the survey disclosed.
A total of 64% still believe Ireland will see a second wave, a quarter now believing the country should introduce more restrictions, and 31% now feel the authorities are trying to return to normal too fast.