With no party claiming an absolute majority, the hunt is now on to form a coalition to try and reach the 80 seats needed for a majority in the next parliament, set to begin on February 20.
"We want to talk to anyone who is interested in delivering a program for government," Sinn Fein leader Mary Lou McDonald told national broadcaster RTE, following the result.
"A government that people relate to, that is in tune with the realities of people's day-to-day lives, not one that is aloof and adrift from the experiences of citizens."
Sinn Fein has already begun talks with several smaller left-wing parties but forming a coalition government with the larger parties is set to be more difficult.
Prime Minister and Fine Gael leader Leo Varadkar acknowledged the shift to "a three-party system" on Sunday and said talks between the parties could be protracted and difficult.
Finn Gael repeated it would not go into coalition with Sinn Fein because of its past links with the IRA. Fianna Fail leader Micheal Martin on Sunday declined to repeat his previous refusal to consider forming a coalition with Sinn Fein.