Italy would like to leave the door open for eventual cooperation with Bulgaria in ferreting out any accomplices in last year's assassination attempt on Pope John Paul II.
''We will never get to the bottom of the case unless we have the cooperation of other countries,'' said the chief investigator into the case, Judge Ilario Martella.
Relations between Italy and Bulgaria have been stretched to near breaking point as Italian magistrates investigate the links between the convicted Turkish man who shot the Pope, and Rome-based Bulgarians who allegedly gave him the orders.
More important, the ''Bulgarian connection'' may ultimately involve Italy's relations with the Soviet Union. ''This matter cannot be discussed without implicitly raising the Soviet question,'' a well-informed diplomatic source said. It is widely believed in political circles that the relatively small Bulgarian secret service is controlled by the Soviet Union's KGB.
The idea that the Soviet Union is behind the plot to kill the Pope has long been a popular theory in the Vatican. The Bulgarian connection was being discussed almost immediately after the Pope was shot in May, 1981.
''At the Vatican, they are convinced that the Russians are involved in the plot to eliminate the Pope,'' US Sen. Alphonse D'Amato (R) of New York told the Italian magazine Panorama last week. Mr. D'Amato, who has close ties with the Vatican, also reportedly said he saw a letter written by the Pope to Leonid Brezhnev threatening to go to Poland and fight alongside his compatriots should the Soviet Union invade Poland. The Vatican has denied that the Pope wrote such a letter.
Subscribers to the theory that ''our Eastern friends sponsored the exercise, '' have reasoned the Soviet Union and the entire Eastern bloc were threatened by the growth of the Polish trade union Solidarity, which Pope John Paul II virtually nurtured into existence. Killing the Pope would have been one way to deal an effective blow against the trade union, which has since been outlawed.
But Vatican prelates are also deeply aware that the church's ''Ostpolitik'' with regard to the Eastern bloc under the direction of this Pope also poses a dangerous challenge to the communist regimes. ''The church's Ostpolitik has changed dramatically under this Slavic Pope, who was born and raised under a communist regime,'' says Bogdan Scciajkowsky, professor of comparative communism at the University of Cardiff and a close observer of the Vatican.
Bulgaria, which has a tiny Catholic population and few problems with labor strikes, would be the least likely country in the Eastern bloc to feel threatened enough by the Pope to strike on its own, Scciajkowsky says.
The Bulgarians have announced they are launching their own investigation of the shooting of the Pope, a move an Italian official dismissed as ''a publicity stunt.''