However, senior Government figures are understood to be reluctant to consider the idea of another full lockdown.
Senior sources told The Irish Times that the possibility of another full lockdown came up during informal discussions in the last few days.
Government figures cited social and economic reasons as to why another lockdown could not happen.
The National Public Health Emergency Team (NPHET) did not recommend a full lockdown in its advice to Government on Monday.
However, senior sources told The Irish Times that the question of a full lockdown will resurface if the number of new cases continues to increase.
“NPHET are certainly making it clear that if this [the measures announced earlier this week] doesn’t work, it’s back to lockdown,” said a source close to Government.
Two further deaths and 54 additional Covid-19 cases were confirmed in Ireland yesterday.
The death toll stands at 1,775 from a total of 27,547 cases.
Of the new cases, 67 per cent are aged under 45, and 27 are associated with outbreaks or are close contacts of a confirmed case.
Nineteen of the new cases were recorded in Dublin, eight in Kildare, five in Tipperary and the rest of the cases are in Carlow, Clare, Donegal, Kerry, Kilkenny, Laois, Limerick, Longford, Louth, Meath, Offaly, Waterford and Wexford.
Responding to concern over the rising numbers of infections in Ireland, acting chief medical officer Dr Ronan Glynn gave a breakdown of where cases had been coming from over the past two weeks.
In a series of tweets, Dr Glynn said: "Workplace outbreaks have been well documented and the large ones in meat and other food businesses account for about 360 of the cases reported in recent weeks.
"Another 40 cases have been linked to the construction sector recently. As you may be aware, we also had six clusters linked to direct provision over recent weeks, with about 90 cases linked to these clusters.
"However, these outbreaks are just part of the story. For example, while they account for approximately 500 cases between them, we have had over 1,200 cases reported in the last 14 days alone.
"So where are the rest of the cases coming from? Well last week we had approximately 75 clusters in families or extended families.
"About 3% or 36 cases over the past 14 days have been travel related, over 200 have been confirmed as community transmission and a further 200 remain under investigation."
Dr Glynn said it was a "collective problem that requires collective action".
He added: "We also need employers and organisations all across society to step up once again and ensure that they have the proper measures in place to create a safe environment for their workers, customers and members alike."