Council staff told the group that a banner promoting its "support services for gay, lesbian, bisexual, transgender, same-sex attracted and gender-diverse young people, their families and communities" was inappropriate at last week's Rediscover the River festival.

Fearing "a potentially toxic environment", Twenty10 – which had been invited by council to set up a kite-making stall – decided to pack up and leave instead.

Its acting managing director, Terence Humphreys, apologised on Facebook for the group's sudden departure.

"We had school-aged clients there, volunteers and staff who were very distressed by the incident," Mr Humphreys said.

"It sends a really horrible message to the people of Parramatta that it wasn't OK to be same-sex attracted, gender diverse in a family event like the Rediscover the River."

Council has been inundated with complaints as news of the January 17 incident has spread. A change.org petition calling for an apology attracted more than 5000 signatures in a matter of hours.

Council said in a statement that organisers asked that two banners be removed "in response to numerous complaints by members of the public", but at no stage did it request Twenty10 to leave.

It declined to say what aspect of the sign was found to be offensive.

"Council regrets any inconvenience or offence taken by its actions and values the efforts and contribution of Twenty10 in servicing at-risk youth," it said.

"Council has enjoyed a positive relationship with Twenty10 over some time and hopes to continue to work in partnership over the coming years."

But Twenty1o is considering lodging a complaint with the Anti-Discrimination Board if it does not get a response from the Lord Mayor, John Chedid.

The request to remove the banners had been made by Cr Chedid's staff, Mr Humphreys said.

"We specifically want an apology and reassurance from the Lord Mayor's office that their staff will undertake some anti-discrimination training," he said.

"To this point we haven't heard back from him."

Councillor and former mayor Lorraine Wearne said she was happy to apologise for any offence caused, but the response – including naming staff on Facebook – was an overreaction.

"These things can generate a life of their own and can feed off themselves and that's what concerns me here – that this is going to be bigger than Ben-Hur with no cause other than the fact that someone asked a stall to please take down a banner," she said.

"If they had [refused to pull] the banner down, that would have been the end of it."

Labor councillor, Julia Finn, labelled the council's request "disgraceful and embarrassing".

But independent councillor, Paul Garrard, said the council had made the right call as the family day was no place for "semi-political" groups.

"They shouldn't have been there, in the same fashion Right to Life weren't there," he said.

"Whether one is for or against the issues the gays were pushing on that occasion, that was not the place to be doing it."

A response is being sought from Cr Chedid.