First results in the European elections are likely to come in the next few hours.
While the final seats in the local elections are also being filled.
There are about 80 seats left to fill in the local elections - with Fianna Fáil set to be the biggest party in local government once again.
Counting is also underway in the European Parliament elections.
Dublin has been through a number of counts already, and could elect the first MEPs by lunchtime.
That is when there are hopes for first counts in Ireland South and Midlands North West.
While Mairead McGuinness could be elected on the first count, it looks like it could be tonight before more candidates are elected.
Reacting to the results, Taoiseach Leo Varadkar said he is not ruling out a general election.
However he clarified he will not be going to the polls in the next few weeks.
Speaking at the RDS count centre in Dublin he said the timing of the election is not necessarily his call.
"In the context of a current Dáil in a minority Government, where we only have a quarter of the seats in the Dáil, that's just the reality of this.
"Of course anybody in government would prefer to be in a government with a stable majority - we don't have that".
Meanwhile the plebiscite on directly elected mayors in Cork is evenly split so far.
Some 5,000 votes have been counted for both Yes and No since 9.00am.
The returning officer is expecting a result around lunchtime.
The first of Dublin's new MEPs is expected to be elected later.
Counting in the Dublin European elections was suspended at midnight on Sunday.
Count staff got through seven rounds of counting on Sunday night, before the announcement that it was ending at midnight.
By that stage, none of the candidates had reached the quota of 72,790.
The closest is the Greens Ciarán Cuffe - who managed 63,849 votes - around 4% less than exit polls were predicting.
He was followed by Fine Gael's Frances Fitzgerald on 59,067.
Rounding out the top five for the four seater constituency: Fianna Fáil's Barry Andrews on 51,420, Independents4Change Clare Daly on 42,305 and Sinn Féin's Lynn Boylan with 39,387 votes.
The first seven candidates to be eliminated were Tony Bosco Lowth, Mark Mullan, Aisling McNiffe, Hermann Kelly, Eamon Murphy, Eilish Ryan and Rita Harrold.
Counting resumed at 10.00am with count eight which is the distribution of Rita Harrold's transfers.
But it could be a late one again as the man in front, Ciarán Cuffe, is still 8,000 votes off the quota.
— European Parliament (@Europarl_EN) May 26, 2019
The first count for the Ireland South constituency in the European elections is not expected until Monday afternoon.
With 750,000 votes to count, it is probably no surprise progress has been slow.
Counting finished up late on Sunday night, and resumed at 9.00am Monday.
Fine Gael's Sean Kelly looks like he will be comfortably re-elected.
Fianna Fáil's Billy Kelleher and Sinn Féin's Liadh Ni Riada also appear to be in strong positions to take a seat.
The Green Party's Grace O'Sullivan is also in with a good chance - but does not appear to be doing as well as expected on transfers.
It could be a race between Independent Mick Wallace, Fianna Fáil's Malcolm Byrne and Fine Gael's Deirdre Clune for the last seat.
But it will not be until the first count late Monday afternoon when we will know who the winners and losers will be.
Reporting by Sean Defoe with Shane Beatty in Dublin and Stephen Murphy in Cork