Eamon Ryan also said he believed the rest of the country could avoid being placed in level 3 restrictions if the public adhered to the Government’s measures.
The Climate Change Minister said there had been no discussion in Government about a nationwide lockdown, rather it wanted to work on a county-by-county basis.
His comments came as the number of people in hospital with Covid-19 continued to rise.
As of 8am on Saturday 134 people with Covid-19 were in hospital, up from 114 on Friday.
A total of 613 new cases of Covid-19 were confirmed on Friday, the highest daily figure in more than five months.
It’s vital to keep connected - but to socialise safely with #COVID19, we have to do things differently to protect ourselves and loved ones.
✅Keep groups small & regular
✅Make a plan to prioritise and reduce your social contacts
✅Meet outside if possible
✅Keep 2m distance pic.twitter.com/u3ikMa0wYP— Department of Health (@roinnslainte) September 30, 2020
“What we’re seeking to do here is not to eradicate the virus, I don’t think that’s going to be a viable option, but to stabilise it,” he told RTE’s The Week in Politics.
“I think that there is real concern when you look at other counties – it is rising very fast. We need to do the simple things, reduce the number of people we meet, avoid social contact.
“If we all do that we can avoid going to level 4, other counties can avoid going to level 3 and I hope that Dublin can get back to level 2 and Donegal too.”
He added that he believed it was possible that the infection rate could be stabilised but he admitted that everyone was “fearful” when the daily numbers continue to rise.
Mr Ryan also said that if counties moved to level 4 restrictions the schools would stay open.
“I think, no matter what, I think the Government is committed that it is important,” he said.
He added: “The international evidence is that it can be done safely and I think our schools have done a good job in terms of making it safe for our students.”
His remarks came as people over 70 and those medically vulnerable were advised to limit their social contacts to a small core group for short periods of time, while remaining socially distanced.
Acting chief medical officer Dr Ronan Glynn said on Friday that the numbers reported over the past week represented a significant escalation in the profile of Covid-19 in Ireland.