Sinn Fein is on 24% and its party leader Mary Lou McDonald is on 52%
The Government is up five points to 46% in the latest political opinion poll.
A Behaviour & Attitudes survey for The Sunday Times also shows the recent steady increase in support for Sinn Fein appears to have stalled.
Sinn Fein is on 24% and its party leader Mary Lou McDonald is on 52% - both unchanged in June.
Meanwhile Fine Gael and Fianna Fáil are both up one point each, to 31% and 24% respectively.
The Taoiseach's own personal satisfaction rating is up 2 points to 55%, while Fianna Fail leader Michéal Martin is up 2 to 49%.
Sunday Times Political Editor Stephen O'Brien says the Mary Lou 'bounce' may have levelled out, but Sinn Fein will still be pleased with today's results:
“Sinn Féin appears for now to have plateaued,” he said.
“Mary Lou remains at 52% unchanged in the satisfaction ratings this month and Sinn Féin remains unchanged on 24% in the state of the parties.
“Now of course, if Sinn Féin got 24% at the next general election, they would be delighted with that.
“If would reap them a tally of somewhere around perhaps 40 or 45 seats.”
He said 40% of the people who voiced support for Sinn Féin are between the ages of 18 and 34-years-old.
“Younger voters who don’t always go to the polls in the same numbers as some of the older demographics although that was reversed – or certainly that trend was bucked – in the recent abortion referendum.”
There was little movement of note among the smaller parties and independent groupings; though non-aligned independents are down one point to 9%.
The poll was taken from May 31st to June 12th in face-to-face interviews with 930 Irish voters.