The Government's up five points to 46 percent 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 on 24% and its party leader on 52% are both unchanged in June, while Fine Gael and Fianna Fail are both up one point each, to 31 and 24% respectively.
The Taoiseach's own personal satisfaction rating is up 2 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, Mary Lou McDonald remains at 52% unchanged in the satisfaction rating this month and Sinn Féin remain 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 - that would reap them a tally of around 40 or 45 seats."
