Sinn Fein on Tuesday became Ireland's second-largest parliamentary party after winning the popular vote in the election at the weekend - shattering the political landscape and thrusting the one-time fringe party with historic links to paramilitaries into a probable role in the next government.

With counting completed in the early hours of Tuesday Sinn Fein had taken 37 of the 160 seats in the next Dail - Ireland's lower house of Parliament - after a turnout of 62.9 percent in Saturday's election.

Centre-right party Fianna Fail was only one ahead on 38, while Prime Minister Leo Varadkar's Fine Gael party took 35, a result likely to mean his departure from office.

More:

If a new government is to be formed when the Dail sits on 20 February it will have to include multiple parties.

Negotiations have already begun, with Sinn Fein arguing for a central role in power after winning 24.5 percent of first preferences in Ireland's single transferable vote system - the largest of any party.

End of duopoly

The breakthrough for the nationalist Sinn Fein party that was once shunned because of its links to Irish Republican Army (IRA) paramilitaries, has broken the stranglehold of two-party politics in Ireland.

Former leader Gerry Adams and other party representatives were even banned from television and radio in the United Kingdom as violence raged over British rule in Northern Ireland over 30 years to 1998.

But with two decades of peace and a new leader under Mary Lou McDonald, Sinn Fein's left-wing policies on tackling crises in housing and health found favour with voters.

Proud to lead. On this day two years ago I was Elected President of @sinnfeinireland This weekend we made history - all of us, together. pic.twitter.com/CWVxZkhLBG — Mary Lou McDonald (@MaryLouMcDonald) February 10, 2020

McDonald said the two main parties - Fine Gael and Fianna Fail - were "in a state of denial" and had not listened to the voice of the people.

On a walkabout in Dublin on Monday she said she had begun talks with smaller left-wing parties to try to "test" whether it was possible to form a government without the two centre-right parties.

"I may well be the next taoiseach (prime minister)," she said before chatting to supporters and market traders.

"Sinn Fein won the election, we won the popular vote ... I'm very clear that people who came out and voted for Sinn Fein have voted for Sinn Fein to be in government," she added.

Varadkar acknowledged the shift to "a three-party system" on Sunday and said talks between the parties could be protracted and difficult.

His Fine Gael party took 20.9 percent, while rivals Fianna Fail took 22.2 percent.

"The Irish political system has to react to it and probably accept that Sinn Fein will be part of the next government," Eoin O'Malley, associate professor at Dublin City University, told AFP news agency.

Appeal to young

Tuesday's result was all the more striking because Sinn Fein ran with just 42 candidates.

Analysts suggest the party may have been taken by surprise by its surge in popularity, and would probably have emerged as the largest party if it had put forward a larger slate.

Fine Gael and Fianna Fail have ruled out any deal with Sinn Fein because of its past associations under Adams, who has long denied allegations he had a leadership role in the IRA.

The armed group fought a decades-long campaign against unionist counterparts and British security forces in Northern Ireland that saw more than 3,000 killed on all sides.

McDonald's policies on tackling wealth inequality and housing shortages appear to have appealed to younger voters among the European Union member state's 3.3 million-strong electorate.

Some 32 percent of voters aged 18-24 and 25-34 backed the party, according to an exit poll on Saturday.

In a sign of the sea change in Irish politics, Varadkar himself was beaten to the first seat in his constituency by a Sinn Fein candidate on Sunday.

He took the second of four seats but it was a sharp blow on a long night for a man facing the electorate for the first time as prime minister.

Varadkar - young, openly gay and mixed-race - has been seen as the face of a new, more progressive Ireland after referendums overturning strict abortion laws and same-sex marriage.