Sinn Féin are up four points to 21% in the Irish Times / Ipsos MRBI poll
Support for Fine Gael has remained largely unchanged - despite the recent turmoil within the party.
A poll in today's Irish Times suggests they have gone up one point since December.
This week's survey puts them on 28% support - just one point behind Fianna Fáil on 29%.
The Ipsos MRBI poll was conducted among 1,200 voters on Monday and Tuesday of this week - before Simon Coveney's remarks on water charges for wasteful usage, but after the whistleblower controversy and the speculation about Fine Gael's future leadership.
The big winners of the poll, however, were Sinn Féin, who are up four points to 21%.
Labour is down two points to 4%, while Independents & others sit at 18% support.
Irish Times political editor Pat Leahy told Newstalk Breakfast that the results should ease the pressure on Enda Kenny.
"Opposition within his own party to the Taoiseach came to a head because they were terrified they were about to be pitched into an election with him as leader," he explained.
"I think that fear will now recede, because on the basis of these numbers there is no great political advantage for Fianna Fáil in calling a snap election."