Agriculture Minister Simon Coveney says the Government is getting a "very strong message" in today's count.
An exit poll carried out for RTÉ this morning predicted Fine Gael would take 24% of the vote in the local elections, and 22% of the European poll.
However, their Coalition partners Labour are facing a much harsher verdict from the electorate.
They could take as little 7% in the local elections and be left with no seats in the European Parliament.
Minister Coveney says that voters' feelings on the parties are clear.
"It's a very, very difficult day for them [Labour], it’s a difficult day for us too in a number of areas," he said.
"I think the Government is getting a very strong message here that people feel that they've had enough of the difficult years and they want progress and they want it faster.
"We have managed, as a Government, to bring stability to Ireland from an economic perspective, but people want to see the benefits of that now."