The Vatican today offered to cooperate fully with the Italian government in untangling its complex relations with the scandal-ridden Banco Ambrosiano and for the first time described how it became involved in financial deals that led to the collapse this summer of Italy's largest private bank.

In a final address to a four-day meeting of the College of Cardinals, Pope John Paul II said, "The Holy See is willing to take all steps that are necessary for an understanding of both sides so that the entire truth will come to light."

Later in the day, the Vatican press office issued an unprecedented seven-page statement that made public the text of a report by Vatican Secretary of State Cardinal Agostino Casaroli on relations between the Vatican's Institute for Religious Works (IOR) -- the official name of the Vatican bank -- and the now-dissolved Ambrosiano Bank.

The report sought to explain the existence of controversial letters of patronage issued by the Vatican bank in favor of the Banco Ambrosiano. The letters later led the Italian government to claim that the Vatican is responsible for as much as $1.2 billion of the Italian bank's debt.

Repeating the conclusions of Vatican lawyers and a three-man commission of outside experts that the Vatican had nothing to repay, the report said that through otherwise normal banking relations the IOR became the owner of two companies and, without knowing it, gained "indirect control" over eight others tied to the first two.

The Vatican became aware of these links in July 1981, the report said, and in September issued communications to two Ambrosiano subsidiaries, the Banco Andino of Peru and the Banco Ambrosiano di Managua, the principal creditors of the companies in question.

But the communications only confirmed the Vatican's legal control, direct or indirect, over the companies. The report said that the Vatican bank issued no guarantees and thus did not create any legal obligations.

"Consequently," it concluded, "operations carried out by those societies prior to Sept. 1, 1981, cannot be considered or presented as effects of the above-mentioned communications."

The report by Casaroli appears to endorse the opinion that the IOR's relations with the Banco Ambrosiano were normal and that, if anything, the Vatican bank had been victimized by Ambrosiano chief Roberto Calvi, who was found dead by hanging in London in July.

The Vatican has admitted to long-standing relations with the Banco Ambrosiano, and last week Cardinal John Krol of Philadelphia, chairman of a special 15-member Vatican finance commission, said the relationship was a normal one because of the Ambrosiano's long-standing and solid reputation.

The Casaroli report restated the Vatican's intention to work with the Italian government to "draw the conclusions that will appear legitimate" based on documents in the case.

It made it clear, however, that future financial relations were to be treated with greater vigilance.

The report made no mention of controversial IOR president, Chicago-born Archbishop Paul Marcinkus. But in a talk earlier with American journalists, New York's Cardinal Terence Cooke said that Marcinkus had not fallen into disfavor at the Vatican because of the Ambrosiano scandal.