Italy moved closer to a freeze in diplomatic relations with Bulgaria this week as Italian investigators pushed ahead in their search to corroborate the story of Bulgarian involvement in the assassination attempt against Pope John Paul II told them by would-be assassin, Mehmet Ali Agca.

In an address to the Italian parliament before easily winning a vote of confidence this week, Italian Prime Minister Amintore Fanfani said his two-week-old government had decided to prolong the recall of its ambassador to Bulgaria.

Ambassador Carlo Rossi Arnaud was summoned back to Rome Dec. 11 for consultations amid press reports alleging a Bulgarian role in the shooting at St. Peter's Square May 13, 1981, and charges of possible Bulgarian involvement in other espionage and terrorist episodes in Italy.

The reports led to speculation about Soviet involvement in the assassination attempt as well. There have also been unconfirmed reports in the press here that Agca and the Bulgarians had planned an attack on Lech Walesa during the Polish Solidarity leader's visit here in January 1981.

In a news conference in Sofia yesterday, the chief Bulgarian prosecutor, Boyan Traikov, invited Italian magistrate Ilario Martella, who heads the investigation, to come to Sofia to question two Bulgarian officials and a Turkish smuggler charged with complicity in the attack on the pope. The three accused men appeared at the news conference and denied any role in the case.

The Soviet Union angrily denied any involvement in the assassination attempt and condemned speculation about an East European role, Reuter reported from Moscow. The statement, first issued by Tass news agency last night, said that "absurd insinuations" were being spread in the West that some Communist states were behind the shooting in May 1981 and that this amounted to a "campaign steeped in lies."

It was the first Soviet comment on the allegations. Tass repeated the statement twice Saturday, and it was printed by Pravda and other Moscow daily newspapers--an indication of the strong Soviet reaction to the charges and the leadership's desire for maximum publicity of it.

Fanfani, in addressing parliament, emphasized the need for cautious handling of the case because of its international ramifications, but said that "the facts now reveal that the time for academic hypothesis is over."

The facts, he added, "stem from observations that the magistrature has verified through tenacious action, beginning from the grave episode of the sacrilegious attempt on the life of Pope John Paul II, which, had it succeeded, would have been the gravest act of destabilization in the world in the last 60 years."

In late November a Bulgarian airline official was arrested in connection with the case, and Italian judicial and Foreign Ministry officials later acknowledged that two low-ranking Bulgarian Embassy officials who have since left the country were also suspected of possible involvement.

According to judicial sources, the story of Bulgarian participation in the attack came from Agca, who is serving a life sentence in a central Italian prison for shooting the pope, and Martella is seeking evidence to corroborate Agca's allegations.

Last Monday Martella traveled to Trento in northern Italy to question one of the defendants in an investigation regarding a large arms and narcotics smuggling ring said to involve both Turks and Bulgarians.

Last week, the magistrate interrogated jailed Italian trade unionist Luigi Scricciolo, who is charged with terrorist involvement and is suspected of spying for Bulgaria.

Unsourced Italian press reports this week said that Scricciolo, who handled foreign affairs for the smallest of Italy's three major unions, spied on Lech Walesa for the Bulgarians and sought to pass to them information acquired by the Italian terrorist group Red Brigades during the kidnaping of U.S. Gen. James Lee Dozier a year ago.

Other press reports have said that according to a Red Brigades' informer, Red Brigades leader Mario Moretti traveled frequently to Bulgaria.

This allegation was rejected by Alessandro Padula, a Red Brigades member currently on trial for the 1978 kidnaping and murder of former Italian prime minister Aldo Moro. "We deny the existence of any exchanges or political relations of any nature with the countries of the Eastern Bloc, with the countries of the social-imperialist area of the Soviet Union," he said.

According to the press reports, Agca has charged that Sergei Ivanov Antonov, the Bulgarian airline employe arrested last month, Bulgarian Embassy cashier Todor Aivazov and Zhelyo Vasilev, former secretary to the Bulgarian military attache in Rome, had helped Agca plan the attack on the pope and had accompanied him to St. Peter's Square the day of the shooting.

Agca also reportedly implicated Turkish smuggler Bekir Celenk in the plot. The three suspects denied the story attributed to Agca in the Sofia news conference.

Celenk is wanted by Italian police for allegedly offering Agca 3 million West German marks in Sofia in July 1980 to kill the pope.

A spokesman for the Bulgarian Embassy said yesterday that the charge of involvement by the Bulgarian and Soviet secret services was "pure invention." Bulgarian first secretary Vassilli Dimitrov said, "Those who believe a political problem can be solved by assassination or other criminal acts are ascribing their own mentality to the socialist countries."

Ambassador Venelin Kozev was recalled to Sofia for consultations Dec. 9, and Dimitrov said he did not know when he would return to Rome.

Thursday, in response to renewed political quarreling over the government's handling so far of what Italians are now calling the "Bulgarian connection," Foreign Minister Emilio Colombo provided new details about recent developments in the probe.

He said that on Nov. 11, 11 days after Martella met with then-prime minister Giovanni Spadolini to report on the implication of Bulgarian citizens and embassy officials in the papal attack, the Foreign Ministry received a request for information on the diplomatic status of Vasilev, who had already left Rome, and Aivazov.

On Nov. 24, one day before Antonov's arrest, Martella asked the Foreign Ministry to request the Bulgarians to waive Aivazov's diplomatic privileges. By the time the Bulgarian ambassador provided a negative answer Dec. 6, Aivazov had already left the country.

Aivazov's departure led to political and press charges that the Italian government "allowed" him to escape. The Foreign Ministry has stressed repeatedly that even if the cashier had not fled he was protected from arrest by his diplomatic immunity. Antonov, as head of the Bulgarian state airline's Italian office, could be arrested because he did not have any kind of diplomatic immunity.

Antonov's two Italian lawyers said yesterday that Antonov has alibis for the day of the shooting and for the previous two days, May 11 and 12, when, according to Agca's story, the Bulgarian accompanied him to St. Peter's Square to prepare the attack.

The alleged Bulgarian connection is providing the two-week-old Fanfani government with its first political test. The four-party governing coalition is sharply divided over how to handle the matter.

Italy has excellent trading relations with the Bulgaria, last year exporting goods worth $138 million to that country. According to Italian press reports, about 776 Italian import-export companies have current dealings with Bulgaria.