The Acting Chief Medical Officer has said the focus as a society must be on three national priorities - protecting public health and the most vulnerable, the resumption of non-Covid health services and the reopening of schools.
Dr Ronan Glynn said the number of cases is likely to rise and fall this week.
He said it was important to "look at the wider trends" of the disease in Ireland, and not just one day of figures in isolation.
Dr Glynn said it would be next week before it is known if measures announced last Friday for Laois, Offaly and Kildare are having an impact and minimising community transmission.
The Department of Health announced an additional 35 cases of Covid-19, and one person has died from coronavirus.
There have now been a total of 26,801 confirmed cases, while the death toll stands at 1,773.
Of the cases notified to the department, six are in Carlow, five in Clare, and the remaining 24 are in counties Cork, Donegal, Dublin, Kildare, Laois, Limerick, Meath, Offaly, Tipperary and Wexford.
Five of the cases have been identified as community transmission and 24 are associated with outbreaks or are close contacts of a confirmed case.
"We must remember that our focus as a society is on three national priorities - protecting public health and the most vulnerable, the resumption of non-Covid health services and the reopening of our schools," Dr Glynn said.
He added: "Every time you choose to avoid a crowd, keep 2m distance, wash your hands, wear a face covering and use the Covid Tracker App, you are making a vital contribution to this shared national effort."
The latest figures from the Health Protection Surveillance Centre show the 14-day incidence of confirmed Covid-19 cases by county, for the last 14 days, up to last Sunday at midnight.
The cases are for every 100,000 people. Kildare had 146.1 cases, Offaly 121.9 and Laois 83.8. At the lower end, Galway had 3.1 cases, Cork 4.1 and Wicklow 4.2.
Nine counties had fewer than five cases; Kerry, Tipperary, Waterford, Kilkenny, Leitrim, Longford, Monaghan, Roscommon, and Sligo.
Where a county had under five cases, the exact figure was not provided by health officials, citing reasons of confidentiality.
Meanwhile, the Government is to begin work next week on a "medium-term plan" to take the country through the next six or nine months of living with the virus.
"As different events unfold there will be different types of responses," Taoiseach Micheál Martin said.
He also said that weekly testing for Covid-19 will be rolled out at all meat plants and Direct Provision centres across the country.
Naas General Hospital confirmed an outbreak of Covid-19 on one ward.
The Tánaiste said people should re-double their efforts in order to slow the spread of the virus and people may have become complacent as cases of the virus decreased.
Leo Varadkar said most clusters of the virus were now occurring in households.
In Northern Ireland, health officials said 48 new cases of Covid-19 were reported and no further deaths.
Northern Ireland's health minister Robin Swann has expressed alarm at the increasing number of cases, with 194 positive tests in the last seven days.
Mr Swann said: "We now have an average of over 27 new positive cases per day compared to approximately three per day a few short weeks ago.
"It is very concerning that nine people have been admitted to hospital with Covid-19, two of which are currently in intensive care units.
"This highlights the continuing threat from Covid-19 and we must all do everything within our power to tackle this."
More than 20 million cases of coronavirus have now been registered across the world, with over half in the Americas.
The re-emergence of Covid-19 in New Zealand has prompted Prime Minister Jacinda Ardern to shut down the capital Auckland.
Four domestic cases were confirmed after the country had been coronavirus-free for 102 days.
Director General of Health Ashley Bloomfield said the four confirmed cases were within one family in South Auckland.
They had no history of international travel and family members have been tested and contact tracing is under way.