Environment Minister Eamon Ryan said he believes Dublin and Donegal can avoid going to Level 4, and other counties can remain at Level 2, if people adhere to current public health measures.
The Green Party leader said "everyone has to play their part" by doing the simple things like reducing the number of people they meet.
Speaking on RTÉ's The Week In Politics, he said he thinks measures that have been put in place in Dublin and Donegal will see the numbers stabilising.
But the minister said there remains "real concern" - particularly when you look at other counties where numbers are rising fast.