The former political wing of the Irish Republican Army, which has recast itself as the main left-wing party, secured 24 per cent of first-preference votes, almost doubling its share from the last election in 2016, early results showed.

That put it narrowly ahead of the party of Prime Minister Leo Varadkar and fellow centre-right rival Fianna Fail in an election analysts see as a seismic shift away from Ireland's century-old, centre-right duopoly.

But Sinn Fein is likely to fall behind at least one of its rivals in terms of seat numbers because it stood far fewer candidates and is unlikely to be more than a junior partner in a government.

McDonald said Sinn Fein would talk to all parties about forming a government and that others should accept their responsibility to do the same.

"I do not accept the exclusion or talk of excluding our party, a party that represents now a quarter of the electorate and I think that is fundamentally undemocratic," she said.

Fine Gael and Fianna Fail, who have between them led every government since the foundation of the state, ruled out a coalition with Sinn Fein before the election.

But although Varadkar reiterated his rejection due to "principle and policy", Fianna Fail leader Micheal Martin declined to repeat earlier refusals to consider a coalition with Sinn Fein, saying only that there were significant incompatibilities on policy.

Sinn Fein has moved on from the long leadership of Gerry Adams, the face of the IRA's war against British rule in Northern Ireland - a conflict in which some 3,600 people were killed before a 1998 peace deal.

Opponents of Sinn Fein say its high spending promises and pledge to increase taxes on the wealthy would discourage foreign multinationals that employ one-in-10 Irish workers.

But some parties have praised detailed policies such as a proposed rent-freeze and the large-scale building of houses by the state to tackle problems with the cost and availability of housing.

Varadkar's Fine Gael, in power since 2011, was in third place on first-preference votes with 30 of 39 seats counted. The 41-year-old premier said it was not certain his party would have more seats than Sinn Fein.

Fine Gael's focus on the fastest growing economy in the European Union and success in negotiating a Brexit deal that avoided a "hard border" with Northern Ireland - with border checks reinstated - failed to capture the imagination of voters more focused on issues such as health and housing.

Varadkar said he would talk to all parties except Sinn Fein about forming a government. The option of another minority government also remains, with Fine Gael or Fianna Fail backing the other from the opposition benches.

Australian Associated Press