The Department of Health has announced that a further three people who had been diagnosed with Covid-19 have died.
There has now been a total of 1,738 Covid-19 related deaths in Ireland.
There have also been additional 6 cases diagnosed, bringing the total number of cases in Ireland to 25,477.
Deputy Chief Medical Officer Dr Ronan Glynn, said: "In June, a total of 31 cases of Covid-19 in Ireland were associated with travel.
"The balance of keeping the disease suppressed in Ireland will continue to be challenging as society and business reopens."
Chief Medical Officer Dr Tony Holohan said the National Public Health Emergency Team is still advising against all non-essential travel.
Dr Holohan said the World Health Organisation has warned that the global pandemic is accelerating.
The WHO said that in the past week, over 160,000 cases have been reported each day.
"The National Public Health Emergency Team will meet again tomorrow as it continues to monitor the spread of Covid-19 nationally and internationally, and review Ireland's response and preparedness to the disease," Dr Holohan said.
In Northern Ireland, no further deaths linked to Covid-19 have been recorded, with the toll there remaining at 551, according to the Department of Health.
There was one new case of the virus confirmed, bringing the total to 5,761.