Green Party TD Paul Gogarty has conceded defeat on Twitter ahead of all the votes being counted in his Dublin Mid-West constituency.
"Loads of 2,3,4, which is comforting, but not enough No.1s," he said.
"I concede, with good grace."
Official counting of the General Election votes began at 9am on Saturday morning.
Statisticians interviewed 3,500 voters after casting their ballots outside polling stations across 43 constituencies on Friday and an RTE poll put Fine Gael ahead with 36.1% of the vote.
The same RTE exit poll in the last general election in 2007 was accurate to within 0.5% of the final result.
Voter turnout was reported to be one of the highest for many years with officials putting the figure in the region of 70%.
Almost 3.2 million voters were registered to cast their ballots, with more than 550 candidates running in 43 constituencies for 165 of the 166 seats.
Ceann Comhairle Seamus Kirk, the Dail speaker, is automatically returned.
The exit poll put support for Fine Gael lower than some opinion polls had suggested, where they had been tipped to secure as much as 40% of the popular vote, potentially allowing for a single-party government propped up by independents.