Earlier this year, as part of Dundee's pound;80 million public private partnership (PPP) scheme to upgrade city schools, it was agreed to extensively refurbish St John's High, making it a "state of the art school", according to Monsignor Joseph Creegan, church representative on the council's education committee.
The city's other two Catholic secondaries, Lawside Academy and St Saviours'
High, are to be amalgamated and relocated in a new building.
The council subsequently withdrew St John's from the PPP scheme and agreed to fund a major refurbishment, costed at pound;10.9 million, from its own budget. When it emerged after a survey by architects that the costs of the planned refurbishment would be pound;13 million, the council stuck to its original figure.
Monsignor Creegan has accused Dundee of "backtracking" on its promise to modernise St John's, claiming that the lower figure would leave older parts of the building untouched.
He said: "If they do not keep their promise they will have broken faith with the Catholic community of Dundee."
But Jill Shimi, leader of the council, denied there was any question of breach of promise. "The council's commitment to spend almost pound;11 million on the school holds good," Mrs Shimi said. "I do not think anyone would question the substantial amount of money that will be spent and this reflects the importance of the project and the tremendous benefits it will bring."
Following discussions with staff and parents on the revised plans, council architects were commissioned to look at all the possible options, Mrs Shimi said, "because it is our intention to deliver the very best for St John's within the budget available".
She would be contacting Monsignor Creegan to discuss the situation at St John's, and to underline the city's "firm commitment" to the Catholic community.