The AILG says around 70 of its female members have been subjected to the calls.
Garda counter-terrorism officers are investigating a series of "disturbing" and persistent phone calls made to female councillors by a man who claims to be a "paedophile" seeking to "make a confession".
The Association of Irish Local Government says it involves repeated calls from an individual who has subjected elected women representatives to inappropriate sexual comments.
It says it has received no reports of male councillors receiving similar calls.
A new survey of female members of the Oireachtas found 96% of respondents had experienced online violence.
Fianna Fail Councillor in Edenderry, Claire Murray is one of an estimated 70 women who was contacted by this person.
She says it's not the first time she's received unwanted attention:
Athlone's Aengus O Rourke is the newly elected President of the AILG and a councillor on Westmeath County Council.
He's asking people not to use a private number when contacting their local politicians:
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