Vote counting starts Sunday, and it could be Monday before the election's results are determined.
However, the exit poll on Saturday forecast a shocking three-way split between the three major parties. Fianna Fail, which oversaw the nation's global bailout in 2010, secured 22.2% in the poll, which has a margin of error of 1.3 percentage points.
"We've never seen a general election result like it".
Varadkar became Ireland's prime minister in June 2017 after an internal Fine Gael leadership contest.
Mr Murphy, who has responsibility for electoral arrangements, made a "special difficulty order" on Wednesday night to ensure the vote in Tipperary will proceed on General Election day on Saturday.
He added: 'In order to form a Government together you have to have roughly the same views around the courts, criminal justice system, around how the economy should be run and also how democracy should function and that is what makes my party Fine Gael not compatible with Sinn Fein'.
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"I'm a good friend of Mary Lou's, she's a very decent person and that radiates".
But as of Sunday evening Sinn Fein's tally had already stunned pundits and upset the dominance of the two main parties - Fianna Fail and Fine Gael - which have run the country for almost a century.
Led by Ms Mary Lou McDonald, the party promised to spend more on housing and health, the two issues which dominated the campaign, close corporate tax loopholes and increase taxes on the wealthy.
"The extraordinary thing is that it seems that the political establishment - and by that I mean Fianna Fail and Fine Gael - are in a state of denial. It's only a few months ago that they were trailing in the polls", he said.
"The people were saying it and particularly the non-government and voluntary organisations".
The election represents a "seismic" shift in Irish politics, McDonald said, with Fine Gael and Fianna Fail facing an unprecedented threat to their stranglehold on power.
"That there appears to be no party large enough to command the support for a majority government will face the Irish electorate with the choice between another, potentially inconclusive election, or a coalition government between a centre-Right party, heavily leaning on global banking and foreign direct investment from U.S., and a hard-Left party, with a less than transparent relationship with its violent past, and whose economic and social policy influences are those of Venezuela and Cuba".
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Rival parties say Sinn Fein has not really changed.
A senior DUP MP has called for a Sinn Fein Stormont minister to quit or be sacked over his controversial claims about a republican murder victim.
"This is a very dramatic election", said David Farrell head of the school of politics and worldwide relations at University College Dublin.
The first seat declared after 4pm was for Donnchadh O Laoghaire, polling higher than Michael Martin, Fianna Fail leader.
It is unlikely any party will win a majority, so the most probable outcome is a coalition or a confidence and supply agreement, like Fine Gael secured with Fianna Fáil following the last election.
Counting of votes cast in Donegal takes place at the Aura Leisure Centre in Letterkenny.
There had been uncertainty on whether the poll in the five seat constituency would have to be delayed after the death of independent candidate Marese Skehan earlier in the week.
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