Votes are still being counted but Fine Gael is expected to be the largest party in the Republic's parliament, without having an overall majority.
The dominant party for generations, Fianna Fail, faces a crushing defeat.
The Irish Republic is the first EU member state to have received a financial bail-out to go to the polls. Mr Kenny said the "exceptional mandate" he had secured would enable him to put his case to other EU countries for changing the terms of the loan.
He said European leaders knew of the difficulties that the Irish people had with the loan package and he saw "room to manoeuvre" over the interest rate. He aimed first to speak to the European People's Party grouping of centre-right parties in Helsinki on 4 March before tackling the issue at an EU summit in Brussels a week later.
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