Support has flooded in from all over the world less than a week after a bid was launched to halt the long-awaited project.
Promoters who have been staging shows at the Assembly Rooms for the last 30 years said they were "amazed" at the strength of opposition to plans which would see theatre spaces used during the Fringe becoming shops and a fine-dining restaurant opened in the heart of the venue.
By last night, some 3,500 people had signed a petition on the Save the Assembly Rooms website, which features video messages recorded by the likes of actors Simon Callow and Brian Cox, and comedians Johnny Vegas and Jo Brand.
Many of those protesting on the campaign's Facebook site, which has attracted 2,215 followers, have accused the council of failing to consult the people of Edinburgh over the plans, which are due to be discussed by councillors today. But councillors responsible for the project have branded the campaign "dangerously misleading" and insist the venue is in "desperate" need of refurbishment.
The historic George Street building is set to close for at least 18 months by the end of the year, ruling it out of use for next year's Fringe. Assembly Theatre, which uses the building as its flagship venue, claims its "magical" atmosphere during the Festival will be lost forever if the project, which will see the loss of five theatre spaces, goes ahead.
William Burdett-Coutts, artistic director of the venue, said: "I am amazed and encouraged by the number of people who have come forward to support the campaign and the feedback that we've had.
"The strength of feeling for the venue is coming out and it's terrible the council is ignoring these views. We just hope that even at this late stage that the council is prepared to listen to what people are saying."
One poster on the Facebook site, Nicola Bunting, said: "I can't believe what I'm hearing, this is absolutely ridiculous! I can't believe that they are actually allowed to do this."
Another supporter, Lauren Jaye Walker, said: "I can't imagine George Street without the Assembly Rooms as they are."
Paul Lister said: "The Assembly Rooms must be saved - they are pivotal to Edinburgh's cultural past and future. This is a beautiful road that remains splendid because of the lack of commercialism - there are shops everywhere else in the city... please maintain the sanctity of the Assembly Rooms."Deidre Brock, the city council's culture leader, said: "The simple truth is this: the Assembly Rooms are now in desperate need of refurbishment. It's true that Assembly Theatre's previous usage of the building's ground floor during the festivals will be affected by our plans, as we will be restoring these parts of the venue to their original retail and dining use. This is essential if we are to finance the vital structural repairs to the principal events spaces upstairs."