There have been no further deaths as a result of COVID-19 in Ireland.
The latest figures also show there are 24 new confirmed cases here.
It brings the total to 1,735 deaths and 22,462 cases.
But Chief Medical Officer Dr Tony Holohan said they are concerned over the number of new cases.
"We are starting to see a worrying trend, with the number of reported cases increasing and some new clusters.
"As restrictions are lifted and people move about more, it’s important that we use the tools that have helped us suppress the virus to date.
"Hand washing, physical distancing, cough/sneeze hygiene and wearing face coverings are important personal behaviours that mean as we go about our daily lives, that we are doing everything we can to avoid contracting the virus and spreading it to those we love."
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 continue to avoid all unnecessary travel at this time."
And Dr Siobhán Kennelly, HSE National Clinical Advisor and Group Lead for Older Persons, added: "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 well-being, but it’s 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."
Dublin GAA footballer Siobhán Killeen has recovered from the coronavirus.
Speaking on Monday, she said: "The aftereffects of this disease are very serious, even for those who are fit and healthy.
"I was in very good health, but it was a very tough battle. I, probably like many others, was naïve in thinking that my age and health would protect me from a very infectious disease."
It comes as Ireland re-opens further under phase three.
Hairdressers, beauticians, restaurants and pubs that serve food were among the outlets which opened on Monday.
It was the biggest re-opening since lockdown began on March 12th.
Gyms, swimming pools and other exercise facilities also re-opened, while all team sports - including close contact sports - can resume.
Museums, cinemas, theatres, bingo halls, galleries and other cultural outlets have also been given the green light.
Churches are other places of worship are also allowed to resume services, which many creches and childminding facilities also re-opened.
Indoor gatherings are currently limited to 50 people with social distancing, while up to 200 people can gather outside.
Face coverings will be compulsory on public transport as capacity increases to around 50% of pre-COVID levels.