Sinn Féin has risen four points and unaligned independents have also grown in the public's affections in the latest Behaviour & Attitudes opinion poll for The Sunday Times.
Fine Gael and Fianna Fáil are down two points each, but Micheál Martin's party retains its strong five-point lead over Fine Gael and is the most popular party, six months after the general election.
The Sinn Féin rise comes near the end of a long parliamentary recess and following a vigorous public debate about the EU's ruling that Apple owed the Irish state €13 billion in back taxes.
The party argued vigorously that the government should not appeal the EU ruling. Fianna Fáil backed the Fine Gael position.
Sinn Féin's Deputy Leader Mary Lou McDonald has welcomed the latest figures - and has again addressed questions around her own leadership ambitions.
Speaking on Newstalk's Sunday Show, she said: "There is no contest at the moment - Gerry [Adams] is our leader, I support him, I have confidence in him.
"When the time arises, yes I would like my name to be considered - I've never made any bones about that, I don't make any secret about that [...] I also accept that there will be others who have an interest, and I hope that whenever the time arises that it won't be a case of this sharpening of knives."
The poll was also conducted during a week when John Halligan, the Waterford TD and Independent Alliance member, threatened to pull out of government over the finding of a clinical review that a second cath lab was not justified for University Hospital Waterford.
Despite tension in government on the Apple and hospital issues, the coalition has risen six points in the satisfaction ratings.
Halligan's Independent Alliance remains unchanged at 4% in the 'state of the parties' index, but other smaller parties have lost support while 'stand alone' independents are up four points.
The face-to-face poll was conducted September 4-14 on a representative sample of 911 Irish voters. The margin of error is 3.3%.
Stephen O'Brien, Political Editor with The Sunday Times, said: "There are some contradictory findings. Fine Gael are down two points, but Enda Kenny is up two points.
"Sinn Féin is up four, but Gerry Adams is down five. So there are some contraindicating findings," he added.
State of the Parties
Fianna Fail 28 (-2); Fine Gael 23 (-2); Sinn Fein 18 (+4); Independent 12 (+4); Labour 7 (+1); Ind Alliance 4 (nc); AAA/PBP 4 (-1); Greens 2 (nc); SocDems 1 (-1); Workers Party 1 (-2).
Satisfaction ratings
Government 36 (+6); Micheál Martin 48 (-2); Enda Kenny 33 (+2); Brendan Howlin 39 (-4); Gerry Adams 33 (-5).
