Voters punished Kenny's Fine Gael party and its junior coalition partner Labour, stripping dozens of lawmakers of their seats.
With all but 10 seats declared, the two parties had just 53 seats between them -- leaving them short of the 80 required for a majority and raising the prospect of a second vote if no deal can be reached.
"The people have spoken, it's going to take a while to figure out what exactly they have said," said outgoing Fine Gael junior minister Simon Harris after he was re-elected.
The results left only one clear grouping for a majority: Fine Gael and runners up Fianna Fail, long bitter rivals that have fought each other to take turns in government since 1932.
Any such deal would face significant opposition within the parties.
"I don't think there's any chance that Fianna Fail would be coalescing with Fine Gael," said Timmy Dooley, a senior Fianna Fail politician told public broadcaster RTE.
Weeks of uncertainty could lie ahead and the first test of whether a government can be formed will be March 10, when the newly-elected deputies are due to meet in the lower house of parliament and try to appoint a prime minister.
Noel Whelan, a political analyst and former Fianna Fail politician, predicted that both Kenny and Fianna Fail leader Micheal Martin would be put forward but fail to get enough support to be appointed.
The swing to anti-establishment and anti-austerity parties echoed recent election in other eurozone countries like Spain and Portugal which have produced political uncertainty.
Market reaction was muted, with 10-year Irish government bonds almost unchanged and the main Dublin stock index down only slightly.
"The Irish bond market reaction has been remarkably muted," said Brenda Kelly, head analyst, London Capital Group, noting however that this could be more down to expected stimulus by the European Central Bank "than any real confidence" in Irish politics.
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