Limerick Independent Councillor Elisa O'Donovan has written a letter to the Green Party Executive Committee calling for "zero tolerance" of sexism in public life.
Cllr O'Donovan was described as "unhinged" and "fame hungry" in a series of WhatsApp messages shared by a number of people, including Green Party TD for Limerick Brian Leddin.
Mr Leddin has apologised for the remarks, made a number of years ago, but has not been sanctioned by the Green Party.
Green Party leader Eamon Ryan said there was no space for commentary that was demeaning of the other person even in a private messaging group.
He said he has spoken to party Mr Leddin at length over the deputy's derogatory comments.
Cllr O'Donovan described her experience as "very distressing".
The speech and language therapist said: "There is an opportunity to really address the unfairness that women in politics experience.
"To have a meaningful discussion about what sexism in politics looks and feels like to those it is directed at.
"If we want to improve the participation of women in politics, then making it a safe place for us to work in must be the starting point."
Cllr O'Donovan added: "All I want is a level playing field. A place where I will not get criticised for things that my male colleagues get praised for."
Hazel Chu, Green party chairperson and former Lord Mayor Dublin, has acknowledged that she has received a copy of Cllr O'Donovan's letter and said that she will ask for the Green Party executive to reflect on it.