Christchurch city councillors are urging the representative at the centre of inappropriate message allegations to make themselves known.
An independent investigation began on Monday, into a complaint of inappropriate social media messages sent to at least one young person.
Radio New Zealand reported the messages said things like "I want a hug" and "I miss you". A meme "sexually explicit" in nature was also sent.
In a statement to Newshub, Christchurch City Mayor Lianne Dalziel said she expected the councillor concerned to make a statement on Monday.
"I've called on the councillor concerned to name themselves in fairness to everyone including their colleagues and the voters."
Papanui councillor Mike Davidson said the allegations were damaging to all councillors, especially at the beginning of an election period.
"I just urge the councillor to come forward," he said following a council meeting on Monday. "Because I don't think it's fair on any of the other councillors that now have a cloud over top of them."
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Heathcote councillor Sara Templeton also said the allegations were a "shock".
A youth group first raised the allegations in May, and a formal complaint was made earlier this month.
According to RNZ, the three complainants were aged between 13 and 21-years-old and the messages were sent over three years.
The independent investigator will do a "preliminary assessment" to determine whether a full investigation is warranted, acting chief executive Mary Richardson said in a statement to Newshub.
"I have discussed these steps with the complainants' representative and I have also kept the councillor informed of the actions I am taking.
"In fairness to everyone involved, I will not be making any further comment while this complaint is being assessed."
Newshub.