A number of Labour councillors have said that a change in party leadership should not be the focus of the party.
It comes after four councillors called for Brendan Howlin to step aside as party leader.
Councillors Pamela Kearns, Noel Tuohy, Mick Duff and Terry O’Brien all called for Mr Howlin to step aside.
Mr Tuhoy, a councillor based in Portlaoise, said that the party was "sleepwalking towards oblivion" if it did not change its leader.
However in a statement, 16 Labour councillors said that instead of focusing on a change in party leadership, efforts should be made to campaign on issues such as housing, precarious work, childcare and free education.
The statement said: "The utterances of the last few days do not have the support of all Labour Councillors and while we do support full membership engagement in any leadership election, we do not feel this is the right time for a change.
"What we need now is focus on the policies outlined above and a frank and open discussion with membership about the future of the party."