Enda Kenny has conceded that it is unlikely Fine Gael MEP Jim Higgins will retain his seat in the European Parliament.
Counting is continuing of the 670,000 ballots in the Midlands Northwest constituency.
Luke Ming Flanagan is favourite to take top spot, with Mairead McGuinness expected to retain her seat.
Fianna Fáil and Sinn Féin candidates and Independent Marian Harkin will be fighting for the last two seats.
The Taoiseach has conceded that Jim Higgins is unlikely to keep his seat, saying: "Jim higgins has been an outstanding and committed member of Fine Gael for many years. While votes haven't been counted, t looks as if Jim is going to be in difficulty here…I thank him for his services to his party and country."