Sinn Féin's Lynn Boylan is on course to top the poll and possibly be elected on the first count in the Dublin European elections.
Twelve candidates are vying for three seats in the city.
The fight for the remaining two seats is set to be close, with Fine Gael Junior Minister Brian Hayes and the Green Party leader Eamon Ryan among those battling it out, along with Independent Nessa Childers and Mary Fitzpatrick of Fianna Fáil.
Sinn Féin deputy leader Mary Lou McDonald says it is clear from the tallies in Dublin that voters are looking for a new approach.
"Its quite an achievement particularly given that the constituency is now a three-seater," she said.
"But we could feel in the course of the campaign right, across Dublin and beyond, a real sense that people, having thought about things, wanted a real substantive change, not just a change of personnel, but a change of politics.
"I think the message for Government couldn't be clearer - and I really hope they hear it."