The organiser of a protest over Island Bay's botched cycleway is refusing to apologise for the use of a Nazi slur.

Vicki Greco led a march through the Wellington suburb yesterday against the latest plan to fix the cycleway.

Wellington City Council wants to spend $4.1m on what it calls a "common-sense" solution.

But the Island Bay Residents' Association is not in favour of the plan, and wants to see the suburb's parade returned to how it was.

Meanwhile, one of the council's Southern Ward seats is up for grabs after Paul Eagle became MP for Rongotai.

Labour's Fleur Fitzsimons is standing in the byelection alongside Greco.

Fitzsimons said she did not attend the protest but found a sign left by her fence afterwards.

It read "Return of the Third Reich".

This just happened to my house. Totally respect right to protest, have been on hundreds myself but this is a real low.

For the record, I'm in favour of the compromise I Bay cycleway and am focused on bringing the community together but I will call out despicable actions. pic.twitter.com/seiPDzOJuu

— Fleur Fitzsimons (@FleurFitzsimons) December 3, 2017

Fitzsimons said she was with her daughter at the time and was left shaken.

"It's such a vile comparison and we should never use such horrific comparisons in politics in New Zealand."

Fitzsimons said she supported the right to protest but it was completely inappropriate to make comparisons with the Nazi regime.

"If I was organising the protest I wouldn't have tolerated a sign like that in my protest and I think that the people who organised it, or are responsible for the sign, should have a long hard think about it."

Fitzsimons said she wanted a formal apology but Greco said she had nothing to apologise for.

"Everyone's entitled to freedom of speech, everyone's entitled to their opinion, it's not for me to tell people what they can and can't say."

Greco said her husband made the sign and carried it during the protest.

She would not answer questions about how it got outside her fellow candidate's property.

Greco said she had removed several signs from her own property since her campaign started.

"I just take them down I don't make a big drama, I don't make a big deal out of it, I don't make insinuations about other people."

Greco said the sign was about the council's handling of the Island Bay cycleway and was not a personal attack on Fitzsimons.

Mayor Justin Lester said any person running for council should want to be above reproach.

"I'd expect better standards from anybody who is elected to council, or running for council, or even aspiring for council. I'm disappointed by the behaviour."

Lester said he hoped there would be an apology.

"Fleur and her family shouldn't have to put up with that. They're residents in Island Bay, Fleur's run a really positive campaign, it's really disappointing to see."

He said he thought the protest itself was disingenuous.

"We put up a compromise proposal that satisfied 31 out of 34 requests by the residents association. Vicki Greco was in all of those conversations and personally agreed with them, so I'm disappointed at the response."