Both Fianna Fáil and Fine Gael have seen a drop in support
Fine Gael has retained a narrow lead over Fianna Fáil in the latest opinion poll.
The Sunday Times/Behaviour & Attitudes Poll has Enda Kenny's party down one point to 28% but Michael Martin's also drops one point to 27%.
Sinn Féin remains unchanged on 18%, the Labour Party is down one to 4% while Independents and others are up two to 12%.
The Independent Alliance is down one point to 4%, Greens are unchanged at 2% while the Social Democrats and Solidarity/PBP are both down one to 1%.
In terms of party leadership, Simon Coveney has taken a lead over Leo Varadkar for the first time among Fine Gael voters as their preferred successor to Enda Kenny.
Support for Mr Coveney is up two points to 33%, while Mr Varadkar is down six to 28%.
Mr Kenny is Fine Gael's longest serving Taoiseach, having equalled the record of John A Costello. April 20th marked his 2,234th day in office.
It is anticipated the Taoiseach will address the leadership issue at a Parliamentary Party meeting on Wednesday.
Stephen O'Brien is political editor of the Sunday Times. He says the stability is good news for Fine Gael at a crucial time.
"Enda Kenny is seen to have performed well on the issue of Brexit, had an influence on the guidelines drafted by the European Council.
"But domestically (he) is struggling on the issue of the Garda Síochána and establishing confidence in the leadership of Comissioner O'Sullivan.
"Perhaps those issues are cancelling each other out.
"Fine Gael will actually be quite happy with that as they enter into this week - perhaps the final week of Enda Kenny as their party leader".