Earlier this week Historic England published a report recommended that the Shropshire Council HQ is not given listed building status, paving the way for its demolition.
However, after campaign group Save Our Shirehall criticised the move, the Twentieth Century Society has also insisted that the building should be protected from the bulldozers.
The building was opened by the Queen in 1967 and designed by county architect Ralph Crowe.
Catherine Croft, director of C20 Society, said: “Shirehall is carefully sited in relation to Shrewsbury’s imposing monument, Lord Hill’s Column.
"Its linked blocks of varying height are clad in Portland stone and mosaic, whilst its dramatic oval Council Chamber is raised on robust concrete piloti.
"It’s an excellent example of civic architecture which if no longer required by the council should be converted to a new use. It would be a huge loss for both heritage and environmental reasons if it were demolished.
"Turning down the certificate of immunity and listing it would encourage developers to look for imaginative alternatives.”
Save Our Shirehall campaigner, John Crowe, the son of the architect Ralph Crowe, added: “Our aim is to ensure the preservation of the proud Shirehall for the people of Shropshire as our civic municipal centre and for the council’s staff members, many of whom like working there.
"It does really belong to the people of Shropshire and Shropshire Council has responsibility as its custodian.
"Once demolished there can be no possibility of the Shirehall becoming part of Shropshire’s architectural heritage.
“As a student, craving a tan, fitness and payment from a summer holiday job, I was one of a team of seven who worked an ‘all-nighter’ pouring the concrete into the shuttering for those four legs which support the council chamber.”