It comes as a further 219 confirmed cases and two more deaths were revealed in Ireland yesterday.
The number of confirmed coronavirus cases in Cork has risen to 104.
The National Public Health Emergency Team is meeting today to consider whether stricter measures are needed to stop the virus spreading.
It comes after British Prime Minister Boris Johnson last night placed the UK on lockdown, threatening police fines for anyone who ignores new measures including a ban on public gatherings of more than two people.
Johnson said people in the UK could only leave the house to shop for basic necessities and "as infrequently as possible".
In Ireland, there were widespread concerns that social distancing was not being strictly adhered to at the weekend when parks and beaches were busy.
Yesterday, there were queues at McDonald’s in Douglas before its planned nationwide shutdown at 7pm.
The Lord Mayor, John Sheehan, who is a GP, said while he was aware of the implications of a full lockdown, he had come together with the mayors of Galway and Dublin in making the call for Ireland.
Under such a lockdown, he said, people would essentially not leave their homes unless completely necessary, and businesses would shut.
“It would be like what we see on Christmas Day, but without people going out walking,” he said.
The Lord Mayor said there were three main reasons for calling for a lockdown, including the challenge of social distancing, adding that while many people were doing their best, it was proving difficult.
He noted that we already have a “partial lockdown effectively” with the closure of businesses including McDonald’s, cafes, restaurants and more than 100 Bank of Ireland branches.
He said rather than doing this in a “piecemeal way", that all these businesses could be temporarily closed.
The third reason, he said, relates to testing: “The HSE has ramped up its testing, but there is still a delay of 5 to 7 days before someone is tested.
In this time, contacts of those people are still walking around.
He said this meant that in some cases “the horse had already bolted.”
The Lord Mayor said introducing a nationwide lockdown would take the pressure off the HSE and would also reduce the number of contacts someone would have.
He noted that 10 percent of ICU beds are already filled with COVID -related cases, and said this would increase significantly in the days and weeks ahead.