"Clearly the government of Fine Gael and Labour are not going to be returned to office," Kenny, the leader of the centre-right Fine Gael party, told RTE television yesterday.
Early indications suggest that Fine Gael and its centre-left junior partner have been hard hit by continued public anger over years of austerity, despite Ireland recording the fastest growth in the European Union.
Many voters turned to independents and anti-austerity parties, and the country now faces the prospect of protracted negotiations as political leaders try to build enough support to form a new governing coalition.
"Obviously one has to wait now until all the counts are in right across the country to see what the options that must be considered are," he said.
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Fine Gael health minister Leo Varadkar added: "I don't think that the obligation to form a government necessarily falls on us automatically."
The centre-right Fianna Fail appeared to have regained some ground lost when the party was routed five years ago in the wake of Ireland's housing crash and economic crisis.
Fine Gael and Fianna Fail, who have taken turns ruling Ireland since 1932, would likely have enough seats between them to form a coalition government.
But despite their political similarities, they are bitter rivals whose differences date back to a civil war almost a century ago.
Initial results showed a turnout of 65 per cent, down from the previous election, and the first 41 out of 158 seats to be filled indicated a fragmented political landscape.
Sinn Fein were set to increase their seats to become the third largest group in parliament, continuing an upward trend in support for the party led by Gerry Adams.
It was once seen as the political wing of the Irish Republican Army but has transformed itself into an anti-austerity force south of their power base in Northern Ireland.