Support for Fianna Fáil has increased by three points to 19%, the latest Sunday Independent/Ireland Thinks Opinion Poll suggests.
Fine Gael has seen a drop of two points to 20%, while the Green Party has seen a one-point drop to 3%.
The poll, carried out on 5 and 6 May, indicates that Sinn Féin remains the most popular political party at 31%, unchanged from last time.
Meanwhile, support for the Social Democrats has fallen by two points to 5%, according to the poll which had a sample size of 1,175 people and a margin of error of plus or minus 2.9%.
Labour and Solidarity/People Before Profit have both seen a one-point increase in support to 4%.
Aontú has seen a fall of 1 point to 2%.
Independents and others are up three points to 13%, according to the poll.