The second day of counting in the European elections gets under way later on Monday.
The count ended on Sunday in Ireland’s three constituencies without any MEPs elected.
The Green Party’s Ciaran Cuffe topped the poll in the Dublin constituency with 63,849 votes. He is expected to be elected later today.
The voting system — single transferable vote — in the European election means counting could run on until Wednesday.
The first day of counting saw a major surge in support for the Green Party with candidates expected to take seats in all three constituencies.
Taoiseach Leo Varadkar said he is confident his party will take three seats adding he was “on the hunt” for two more.
Mr Varadkar said he could not rule out the possibility of an early general election, adding that it will happen when it is the “best time for the country”.
The Fine Gael leader said that the dissolution of the Dail may not be his decision as the main opposition party Fianna Fail could pull the plug at any time.
He also played down talks of going into a coalition with the Green Party.
The Green Party’s Ciaran Cuffe topped the poll in the Dublin constituency with 63,849 votes.
Fine Gael’s Frances Fitzgerald polled 59,067 votes, while Fianna Fail’s Andrew Barry gained 51,420 votes.
Independent Clare Daly gained 42,305 votes, beating Sinn Fein’s Lynn Boylan who polled 39,387 votes. Former SDLP leader Mark Durkan polled 16,473 votes.
No one was elected on the first count in Dublin.
Arriving at the count centre in the RDS Simmoncourts before the first official results, Ms Boylan said she still believes she has a “fighting chance” of taking a seat in the Dublin constituency.
Her party leader Mary Lou McDonald said they were there in a “spirit of optimism and a spirit of hope”.
Sinn Fein is facing challenging results in Ireland in both the European and local elections.
Speaking in Dublin, Ms McDonald said: “We are here to see what will transpire, we know this is a tight race.
“Everybody knew this was going to go down to the wire from the beginning.
“What we have is exit poll data so we are here to get the real figures.”
While counting continues across Ireland, no candidates have been elected in any of the three consistencies.
Green Party leader Eamon Ryan said the surge is “reflective of a green wave of thinking that’s happening all over the world”.
Fine Gael leader Mr Varadkar interpreted the Green surge as a signal from the electorate that they want the government to “do more on climate action”.
But he added it has been a very good election for his own party, with its vote up by around 7%.
Speaking in Dublin, he said: “Our vote is up in all three constituencies. We’ll be ahead of Fianna Fail and they actually beat us in a popular vote in the European elections the last time.”
Fine Gael minister Regina Doherty said she hopes her party can secure a second seat in the Midland/North West constituency.
“Judging from the exit polls, I think the response to our candidates was very good,” she said.
“We are in the hunt for a second seat in the Midlands/North West, and I think that is a genuine response not only to Mairead McGuinness’s representation but also the calibre of Maria Walsh.”
Irish voters will elect 13 MEPs, however two will face an uncertain wait over when they can take their seats due to the Brexit delay.
The Republic will receive two of Britain’s 27 seats when it leaves the EU. They are being redistributed among 14 member states.
The UK is participating in the poll, with British MEPs set to attend the inaugural plenary session of the new parliament on July 2.
As a result, those elected in last place in Ireland’s Dublin and South constituencies must wait to see when they can take their seats.
Local council elections were also held across Ireland on Friday, and counting in those races is continuing on Monday.
Meanwhile, a landslide Yes vote to liberalise Ireland’s divorce laws was confirmed in the early hours of Sunday.
Justice Minister Charlie Flanagan is now set to bring forward a Bill to amend Section 5 of the Family Law (Divorce) Act 1996 to reduce the minimum living apart period to two years during the previous three years.
The European election count for Ireland’s three constituencies — Dublin, South, and Midlands-North-West — started on Sunday morning at centres in Dublin, Cork and Castlebar, Co Mayo.
A Europe-wide embargo meant the first results in the poll could not be declared until 10pm.
The European and local government elections are the first electoral test for Ireland’s main parties since the inconclusive general election of 2016.
The result delivered a hung parliament and precipitated months of negotiations between Fine Gael and Fianna Fail, two parties with a century-old enmity dating back to Ireland’s Civil War.
A historic accord emerged that saw Fianna Fail agree to support a minority Fine Gael-led government through a confidence and supply deal for three years.
The parties renewed that arrangement late last year, extending what has been dubbed an era of “new politics” until early 2020.
While Friday’s elections focused on European and council issues, the results will no doubt be interpreted as a public judgment on Fine Gael’s performance in government and how effectively Fianna Fail has managed the delicate balancing act of holding an administration to account while at the same time propping it up.