The council was created by Pope John Paul II in 1981 to oversee Vatican finances.
At Antonelli's death the Vatican finances were found to be in disorder, with a deficit of 45,000,000 lire.
The Torlonia family gained its fortune in the administration of Vatican finances.
The statement was issued after a meeting by a council of cardinals that oversees Vatican finances.
A special commission of cardinals overseeing Vatican finances warned that reserve funds have been exhausted and the deficit will be greater in 1988.
Journalist David Yallop argues that Luciani was planning a reform of Vatican finances and that he died by poisoning; these claims are reflected in the film.
That means disclosure of even basic information about the pope's health, Vatican finances or shifts in Curia policy is sparse.
Cardinal Nicola Canali, responsible for Vatican finances, enquired whether 'once again the preparation of the Council would be entrusted to the Holy Office'.
The letter, signed by a council of cardinals that oversees Vatican finances, paints a bleak picture.
New methods for raising funds and for improving budgetary discipline were studied by the Council of Cardinals, a body that monitors Vatican finances, the press office said.