Dundee City Council leader Ken Guild has said rebuilding the Royal Arch would be a waste of money.
More than 2,000 people have now signed an online petition calling for the arch – demolished in 1964 to make way for the Tay Road Bridge – to be reinstated.
Hundreds of people helped build a cardboard replica of the Royal Arch in Slessor Gardens as part of the People’s Arch art project.
The massive structure was then torn down on Sunday and the boxes trampled by hundreds of delighted children.
The temporary reconstruction of the arch has now led to demands for a permanent replacement to erected.
Signatory Graham White said: “I left Dundee over 60 years ago, but the old Royal Arch, the docks and watching the sand dredgers unloading in front of the bus terminus are among the indelible memories of the place.
“My wife who never saw the real thing has seen old photographs and can’t believe any city would give up such a remarkable landmark. I’d certainly love to see it rebuilt.”
Steven Cox added: “It’s such a disgrace that this beautiful structure was demolished, it would make a nice iconic statement at the new waterfront, but I believe this will stay in the past, and it will never be rebuilt.”
More than 1100 people voted in an online Courier poll over whether or not the arch should be rebuilt.
Of the 1151 votes cast, 866 (75%) supported rebuilding the arch.
However, not everyone is in favour.
Council leader Ken Guild said there are no plans to recreate the Royal Arch or to build on Slessor Gardens.
He said it had been designed to create a space in the city for events likes The People’s Arch project.
Mr Guild said: “That is the whole point of Slessor Gardens. It’s seen as being a venue for various events over the years to come.
“As for rebuilding The Royal Arch, I would not be in favour of that.
“There are far more important things to spend money on.”
Some even branded the suggestion of rebuilding the arch as “selfish and idiotic”.
On the petition comments, Simon Stewart said: “We are in the middle of full on austerity measures and people are talking about putting up a stone arch just so they can re-live their past.
“That is actually selfish and idiotic. Dundee is a city that is moving forward. It doesn’t need to be held back by people who cannot let go of their past.”
And Grant Buttars from Edinburgh said: “I’d be more in favour of a new arch, not a copy of the old one.”