The latest opinion poll by Red C for Paddy Power shows Fine Gael retaining support of almost one third of the electorate.
At 32% it is up on figures released last week but down on what was recorded in March.
Sinn Féin has kept its position as the second biggest party in the country with one fifth of the vote ahead of Fianna Fáil on 18% – down slightly on their highest mark for three years.
Labour continue to be hit hard by the electorate and at 13% are significantly worse off than they were at the general election in 2011. The poll showed the party has lost six points of support since then.
The Independents and the Greens make up another 17% of the voter share.