The Health Minister Stephen Donnelly says there are currently no plans for local lockdowns in parts of Dublin.
It comes after 217 cases were confirmed in Ireland on Tuesday - the highest daily figure since May.
Some 103 of the new cases were in the capital.
But Minister Donnelly told Pat Kenny there are no plans being considered for any lockdown.
"That's not being contemplated at the moment - what we're looking at at the moment is the different healthcare areas within Dublin.
"It's split into eight.
"What we're seeing is that in the north and north-west, really around the border of Kildare, we are seeing higher cases.
"The cases in Dublin generally have been increasing steadily over the last few days.
"We are watching the situation carefully.
"However the national measures that we brought in two weeks ago were for exactly this reason - to say the 14 day incidence rate was gong up, it was going up quite quickly."
"When the green list came in, the 14 day incidence rate per 100,000 for Ireland was about 3.5 - that's now gone up to over 30, so almost 10-times more.
"There has been no talk of additional restrictions being brought in for Dublin, or indeed other areas."
Asked if parts within Dublin could be placed in lockdown, Minister Donnelly said: "It's not being contemplated at the moment, no".
It comes as two pieces of legislation are being brought to Cabinet - to give Gardaí the power to shut premises not complying with COVID-19 guidelines, and to be able to fine people for the same reason.
Minister Donnelly explained: "The big problem we have with law at the moment is the COVID regulations are based on the 1947 Health Act.
"And unfortunately that act has only one schedule for if something is or is not what they call a penal provision: in other words, if there's a penalty attached to it.
"That penal provision is for a fine of up to €2,500 and/or a prison sentence of six months.
"Clearly that is completely disproportionate to the kind of infringements we're looking at, and I would argue is not in the spirit of the solidarity that we've had and that we need.
"So what I'm going to be seeking is amending legislation to essentially insert a new schedule into the 1947 Act.
"So for face coverings, for example, maybe we can have €20 fines, €40 fines.
"For the house parties where we believe there is a genuine public health issue, there are more appropriate fines so we can say it is against the law, there are proportionate penalties for it and we're not relying on this penal provision that is over 70 years old that simply isn't fit for purpose".
In terms of house parties and shutting them down, he said they decided not to attach a penalty to restrictions on gatherings in people's homes.
"It is a legal requirement, but there is no penalty attached to it".
"If we end up in a world where enforcement is required, we will lose the battle against COVID-19 - and one of the things we have seen very strongly in this country is solidarity."
"The approach that has been taken on a lot of the legal requirements that have been brought in to date is as we now have for the gatherings in people's houses.
"[That] is to say that people need to know that is a legal requirement, therefore it is contained in the regulations - however we are not attaching penalties".
"Enforcement is very, very difficult, we don't want a society where people are snooping and spying on each other and the only penalty provision right now is completely disproportionate".
He also confirmed the Government's green list is "under review", but would not be drawn on specifics.