The Chief Medical Officer Dr Tony Holohan has said it will take another week to see if there has been any effect on the incidence COVID-19 from the easing of measures in phase one.
His comments came as there were no new deaths reported due to the coronavirus on Monday.
That marked the first day no new deaths have been reported since March 21st.
However there were 59 further confirmed cases of the virus.
The total number of COVID-19 related deaths in Ireland stands at 1,606.
On Monday Dr Holohan said: "The number of new cases and reported deaths over the past week indicates that we have suppressed COVID-19 as a country.
"It has taken strict measures to achieve this.
"It will take another week to see any effect on disease incidence that might arise from the easing of measures in phase one.”
According to research conducted on behalf of the Department of Health, 61% of people think it likely that Ireland will experience a second wave of COVID-19.
On this, Deputy Chief Medical Officer Dr Ronan Glynn, said: "While NPHET continues to monitor the spread of COVID-19, both here in Ireland and internationally, ultimately it is the collective behaviours of each individual which will determine the course of this disease.
"The importance of regular hand washing, physical distance and cough/sneeze etiquette cannot be underestimated.”
And Dr Siobhán Ni Bhriain, Health Service Executive (HSE) integrated care lead, added: "If a person is experiencing symptoms of any condition, including symptoms associated with conditions for which there are screening programmes, it is important to make early contact with you doctor and not await a routine screening appointment.
"GP clinics have remained open throughout the pandemic and will continue to be available to the public in these circumstances."
Meanwhile the number of patients self-isolating in City West Hotel in Dublin has dropped below 100 for the first time.
The centre was opened by the HSE on April 1st for people who cannot self-isolate at home.
Dr Ni Bhriain said the number of people went below 100 this week "for the first time".
"More or less we did have 150/160 previously."
She said while she did not have an exact figure, it stands at "around 80 at the moment".
Data of all cases, as of midnight on Saturday, reveals:
- 57% are women and 43% are men
- The median age of confirmed cases is 48 years
- 3,225 cases (13%) have been hospitalised
- Of those hospitalised, 394 cases have been admitted to ICU
- 7,842 cases are associated with healthcare workers
Dublin has the highest number of cases at 11,876 (48% of all cases) - followed by Cork with 1,438 cases (6%) and then Kildare with 1,390 cases (6%)
Of those for whom transmission status is known community transmission accounts for 59%, close contact is 38% and travel abroad accounts for 3%.
