Sinn Féin president Gerry Adams has said he would not be as foolish as Enda Kenny and say when he might step down as leader of the party.
He was speaking at the commencement of a party consultation process in Dublin to develop its strategies for the next decade.
Asked about yet another call for him to stand down, he said the party is democratic and all issues are open for debate.
Standing alongside him, Northern Ireland's deputy first minister Martin McGuinness said that Mr Adams enjoys overwhelming support from Sinn Féin.
A party cumann chair in Cavan, Thomas Anthony McNulty, had called for Mr Adams to retire, according to a report in The Irish News.
Enda Kenny has indicated he will not lead Fine Gael into the next general election, triggering much recent debate about his future in the party and media.
The Sinn Féin meeting in Ballyfermot is the first of 46 gatherings to take place over the next week.
Mr Adams said: "This democratisation of our strategy formulation is an opportunity for the national and regional leadership of Sinn Féin to set the agenda and map out our aspirations and ambitions for Ireland over the next decade, as we continue to work towards Irish unity and transformation of Irish society, north and south".
Mr McGuinness has said there is huge dissatisfaction in Northern Ireland in the wake of the Brexit vote.
He continued that there is alarm across most sectors, including among the business and university communities.
He said there is a growing view that politicians in London do not "give a damn" about the people of the North.
