Senior figures in Fine Gael 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 Fail 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 Tanaiste (deputy prime minister) 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 Fail 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 Fein 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.
He predicted his party would double its number of seats in the Dail parliament 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 Fail figure Conor Lenihan, who stood in Dublin South-West, was one of the first to admit defeat.
"Clearly the tide was out for Fianna Fail in Dublin," he said.
Mr Lenihan, a former junior minister who comes from a powerful Fianna Fail 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."
Later, Mr Varadkar took the second seat in Dublin West, leaving Mr Lenihan and Mr Higgins to take the final seats.
The decimation of Fianna Fail saw other leading figures line up to admit the damage.
Pat Carey, outgoing Gaeltacht Minister, said: "There's no shame in losing - the shame will be if we didn't learn from it."
The party, which has been in power for 60 of the last 80 years, oversaw some of the strongest years of the Celtic Tiger, but was also roundly blamed for the devastating recession of the last three years.
The intervention of the IMF, 6 billion euro (£5.1 billion) budget cuts and politic chaos of ministerial resignations and the pull-out of the Greens in the final days of government combined to anger the electorate.
Fianna Fail support in Dublin was even forecast to fall from 18 seats down to as low as one - Mr Lenihan the only hope of success.
Junior minister Peter Power also accepted that the vote had collapsed in Limerick.
Noel Dempsey, a former Fianna Fail minister who retired from politics, said a nationwide total of 20-plus seats was all the party could hope for.
"It's looking pretty grim," he said.
"And to get a result in the low 20s would be good."
Analysts suggested that Fine Gael's seats could run into the mid-70s, just shy of the necessary majority.
Fine Gael's deputy director of elections Frank Flannery said that, if the exit poll is accurate, the election will mark a historic occasion.
"From my party's perspective we will be far and away the biggest party in the Dail for the first time ever," he said.
"It's a pretty disastrous poll from Fianna Fail's point of view."
He told RTE Radio that Fianna Fail could have a "dramatically horrific election".
Aengus O'Snodaigh, Sinn Fein's candidate in Dublin South Central, ruled out working with Fine Gael in government.
"Fine Gael have virtually the same policies as Fianna Fail - in fact, much worse - so I cannot see any situation where Sinn Fein would work with Fine Gael.
"We've stood on this platform of trying to promote an alternative way and Fine Gael have not expressed that so I cannot see that happening."
A clearer picture will emerge later tonight when the second and third seats in constituencies start to fill.
Other significant results included guaranteed success for campaigning Senator Shane Ross, one of the most high-profile Independent candidates and on course to top the poll in South Dublin.
Developer Mick Wallace was also topping polls in Wexford, according to tallies.