A Vatican financial statement, made public by the National Conference of Catholic Bishops for the first time in history yesterday, shows that the administrative headquarters for the world's 840 million Roman Catholics had an operating deficit of $56,723,375 for 1986.

The decision to make a public disclosure after nearly 2,000 years of secrecy was made last October by a 15-man council of cardinals who expressed hope that such openness would stimulate the faithful to greater generosity, according to Cardinal John Krol, one of two Americans on the council.

"We need complete accounting," Krol reported to U.S. bishops at their annual meeting here last fall. "It's the only way to go."

The deficit was met by dipping again into Peter's pence, the annual worldwide collection for the Vatican, taken each June in this country, and the only direct channel of support from the faithful. It accumulates year to year.

In 1986, Peter's pence contributions totaled $32,031,914. To meet the deficit, church officials took $24,691,461 from the fund's reserve. Partly as a result of repeated pleas for help, the collection for the first nine months of last year totaled $35,797,571.

Peter's pence, established in the 8th century, is intended to fund works of charity authorized by the pope. Church officials have expressed increasing concern that not only the fund's entire annual income but also portions of its reserve, which totaled nearly $25 million in 1986, are now required annually to maintain the Vatican.

Unlike individual dioceses that finance their activities by the equivalent of an annual head tax on individual Catholics, the Vatican must rely solely on voluntary contributions through the Peter's pence collection.

Of Vatican expenses totaling nearly $114 million in 1986, the largest was $58 million for personnel. Explanatory notes said the 2,395 employees were paid $50,638,788. Coincidentally, Vatican lay employees yesterday announced plans to demonstrate next week for higher pay.

In addition, pension payments to 885 retirees totaled $7,290,866 in 1986. Such payments must come from operating expenses since the Vatican has no self-sustaining pension fund.

Other major expenses included $11,681,421 for publishing, $11,002,994 in expenditures related to investments, $10,360,919 for equipment and operating costs of Vatican Radio and $9,716,689 for administrative expenses.

The latter category lumps many items, ranging from stationery and printing supplies to costs associated with holding of worldwide synods of bishops.

Income came largely from investments ($38,829,334 before costs), publishing activities ($17,080,157), miscellaneous income from departments in the Vatican bureaucracy ($6,119,463), utilization of endowment funds ($3,491,127) and Vatican Radio ($1,251,047 from sale of tapes of papal speeches and radio programs).

Soaring Vatican expenses are largely an outgrowth of changes in the church in recent decades. Modernization spurred by the Second Vatican Council in 1962-1965 required establishment of several commissions, secretariats and other units, all of which involve meetings annually or more frequently of bishops and consultants from around the globe.

In addition, recent popes have worked to internationalize the church bureaucracy. With many of the new leaders coming from impoverished parts of the world, the Vatican has been required to pay for their travel and housing in Rome. The pope's worldwide travels are generally paid for by the church in the countries he visits.

A lesser but still significant factor for the Vatican, which has grown increasingly dependent on contributions from its affluent American branch, has been the decline in the value of the dollar.

While scandals involving the so-called Vatican Bank have raised painful moral and ethical questions, they are unrelated to Vatican deficits since the bank, known as the Institute of Religious Works, is a separately chartered institution.

Krol, who retired last month as head of the Philadelphia archdiocese, continues to head special efforts to raise contributions from wealthy American Catholics, in efforts other than Peter's pence, to alleviate the annual deficit.