Senior figures in the Fine Gael party have claimed they could be on course for single-party government.
Taoiseach-in-waiting Enda Kenny is on the verge of a series of historic successes paving the way for power alone, or with the backing of independents or a resurgent Labour Party.
The ruling Fianna Fáil party has been annihilated by angry voters.
Two of its most high-profile Cabinet members are on the ropes as they fight for the last seats in former heartlands – Finance Minister Brian Lenihan in Dublin West and Tánaiste Mary Coughlan in Donegal South-West.
Another two ministers, Mary Hanafin and Barry Andrews, are destined to lose in Dun Laoghaire as analysts and party advisers warn Fianna Fáil will be lucky to get 20-plus seats.
Phil Hogan, Fine Gael’s director of elections, warned that no-one should rule out single-party government.
“Anybody that writes off so early in the day... I think they’ll probably get a fright as the day wears on,” he told RTE Radio.
The first TD elected was Labour‘s finance spokeswoman Joan Burton, who topped the poll in Dublin West.
Her victory left Mr Lenihan fighting it out with Fine Gael’s Leo Varadkar and Socialist Party MEP and United Left Alliance member Joe Higgins for the last two seats.
Sinn Féin president Gerry Adams was on the verge of topping the poll in Louth after giving up his Westminster seat for West Belfast to run in the Republic of Ireland.
He predicted his party would double its number of seats in the Dáil where it won four seats in 2007, before it added a fifth in the Donegal South West by-election last November.
“I think we are on course to do that,” he said.
He congratulated Fine Gael leader Enda Kenny on the prospect of becoming Taoiseach.
“If Enda becomes Taoiseach, I wish him well,” said Mr Adams.
“We will support him when he is doing things that we think are good and progressive, and we will oppose him tooth and nail when he is doing things that are not in the common good.”
Another senior Fianna Fáil figure Conor Lenihan, who stood in Dublin South-West, was one of the first to admit defeat.
“Clearly the tide was out for Fianna Fáil in Dublin,” he said.
Mr Lenihan, a former junior minister who comes from a powerful Fianna Fáil dynasty, accepted he had seen his support collapse from being top of the poll in the 2007 election.
The Greens looked to have been hit hard for their time in coalition government and it appeared they would only survive if they manage to take the last seats in Dublin South or Carlow-Kilkenny.
Green Party TD Paul Gogarty conceded defeat along with his party colleague Ciaran Cuffe.
Mr Gogarty announced his failure on his Twitter account, adding: “I concede, with good grace.”