"Not on my watch," Kevin Pearcey wrote on the online post. "These gardens are sacred to us Napierites. If you want to destroy it councillors, resign."
Jules Cunningham stated a relocation would "irrevocably change the aesthetics of an icon, taking away so much by adding a modern monolith that can never look like it belongs".
Of particular concern appears to be the squares' place in Napier history - Clive Square was included in the original 1854 town plan, and became a tin town during the recovery years after the 1931 earthquake.
Of further contention was that Memorial Square houses a World War I cenotaph - the council recently came under fire for removing commemoration items from the former Napier War Memorial Conference Centre during its renovation.
Yesterday Napier mayor Bill Dalton said concern expressed online was not reflective of general public opinion, and he did not take account of "the few negative nay-sayers that we see on social media".
The feedback he had received from people in the community was that the relocation was seen as an "idea worthy of investigation".
When asked if he felt the level of concern expressed at this stage in the process sent a message, Mr Dalton said it did not.
"What it does do, is it proves once again the nay-sayers are against everything we try and do."
He said the viewing platform on Marine Parade was a "prime example" of this - it had initially been "rubbished" on social media, but was now a highly utilised facility.
To further address concern, council director city strategy Richard Munneke said the project was "truly in its infancy", and that the library relocation could only happen if it was decided council staff could be located in one building - rather than the two currently.
He said the civic building was no longer fit for purpose, and while council had the budget set aside to upgrade it, "as part of that process we are looking at how to make best use of the entire council site for the city of Napier".
He said they were also considering the library's future, in terms of what libraries would look like 20years from now.
"Nothing is decided, and nothing will be, until we have all the information we need and have taken that info out to the community to discuss in detail."
At this stage, the council had identified "lower Emerson Street" as one possible location. The other option was developing and upgrading the library at its current location.
Part of the online concern stemmed from confusion around the Clive Square project as outlined in the council's City Vision 2015 document, in which images appear to show buildings in the space between the two squares.
The document also suggests "a new park building on Clive Square to mirror the heritage building and define the western side of the park" be considered, but there are no specific details included.