Ireland's governing Fine Gael and opposition Fianna Fail were both claiming on Monday that they could form the next government as the count was ongoing for the final 10 seats to be filled.
"Irish politics is now in a real state of flux," said Charlie Flanagan, the outgoing foreign minister.
Centre-right Fine Gael remains the largest party so far with 47 seats, despite suffering major losses in Friday's election.
Opposition Fianna Fail performed better than expected, gaining 43 seats.
"Everybody has to focus on the formation of the government. But Fine Gael is still the largest party and has the greatest share of responsibility in that regard," said Flanagan, a Fine Gael party member.
He refused to be drawn on whether Prime Minister Enda Kenny would talk to arch rival Fianna Fail about a coalition.
Billy Kelleher, Fianna Fail's director of elections, told RTE's Morning Ireland radio show that the party must fulfil the mandate it sought, which was to remove the present government from office.
Kelleher insisted that Fianna Fail could form a working majority with independents and smaller parties.
Independents won 16 seats and the left-leaning Anti-Austerity Alliance - People Before Profit won five.
The Independent Alliance won four seats and the Social Democrats got three, reflecting a good election for left-leaning parties and alliances. The Green Party will be back in parliament after winning two seats.
Nationalist party Sinn Fein has 22 seats so far, its best result in a general election south of the border. It has also ruled out coalition with either of the centre-right parties.
Kelleher also said Fianna Fail would not be "contacting or formally requesting" support from Sinn Fein in any form.
Labour was struggling to claim a seventh seat Monday, which would give it the number required for speaking rights in the Dail, or lower house of parliament.
The party, Fine Gael's junior partner in a coalition government over the last five years, had a bruising election, with its support plummeting since 2011, when it won 37 seats in the Dail.
Under Ireland's electoral system of proportional representation, in which voters rank candidates by preference, counts can take a long time.
Several recounts were taking place Monday, and a decision has to be reached on disputed votes in Dublin South Central.