Fianna Fáil has secured 43 seats so far in the election count.
Noel Ahern has been elected in Dublin North West, while party colleague Pat Carey looks poised to take the second seat.
The third seat is between Labour's Roisin Shorthall and Sinn Féin's Dessie Ellis.
Green Party leader Trevor Sargent is blaming increased support for Fianna Fáil and Fine Gael for his party's poorer-than-expected performance.
The Greens have increased their share of the vote in this election but it remains unclear whether they will pick up any additional seats.
Deputy Sargent is almost certain to hang on to his own seat in Dublin North.
Sinn Féin's Larry O'Toole is out of the race for a seat in Dublin North East.
As the fourth count gets underway, Fianna Fáil's Michael Woods is still on top. Fine Gael's Terrance Flanagan picked up over two and a half thousand transfers from Brody Sweeney and is now in line for the second seat.
However, it will all depend on O'Toole's transfers. At this stage, no one has been elected in this constituency.
PD leader Michael McDowell earlier conceded defeat in Dublin South East and has quit public life as a consequence.
Lucinda Creighton of FG is elected. Ruairi Quinn of Labour was also returned, along with John Gormley of the Green Party and FF's Chris Andrews.
The decimation of the PDs continues in Dun Laoghaire, where Fiona O'Malley also likely to lose her seat.
The number of seats confirmed nationwide so far is: FF 43, FG 14, Lab 7, PD 1, GP 2, SF 1, Ind 1.