Within days after Mehmet Ali Agca shot Pope John Paul II last year, Italian police said they were convinced that someone had supplied the Turkish gunman with money and other support in the months before the attempted assassination.

In the 16 months since then, however, the inquiry into who was behind Agca has advanced slowly, and there are signs that some of the governments involved would be content if the case languished.

Only one person has been arrested as a suspected accomplice in the shooting, a Turkish youth described as a far-rightist who is charged with passing Agca the gun used in the attack.

Results have been so skimpy that the Italian chief investigator in the case, Ilario Martella, flew into Washington yesterday in hope of evaluating two recent U.S. media reports suggesting that Soviet Bloc intelligence agencies were involved. Martella made clear in a recent conversation in Rome that there was no hard evidence to prove East Bloc involvement, but he said last night in a brief talk on the telephone from his motel near the Pentagon that he could not rule out the possibility.

The major reason for the lackluster progress is the extreme difficulty in uncovering the tracks of Agca, a self-proclaimed "international terrorist" who visited a half-dozen or more countries in the 17 months before the shooting and traveled in the murky world of Turkish neofascist youths living abroad.

Another reason, however, is the lack of a coordinated, international inquiry. Martella indicated in Rome that cooperation from other countries has been uneven, and a U.S. intelligence source said that there had not been much "visible" evidence of international coordination. The U.S. official said that several countries have not been particularly open in providing details about the case, because it could expose them to criticism over their handling of terrorism or could cause diplomatic strains with the Soviets.

Reports last month by NBC-TV and Reader's Digest suggested that the Bulgarian secret service masterminded the shooting on behalf of the Kremlin because of Soviet irritation over John Paul's support for the independent union Solidarity in his native Poland.

In interviews with correspondents for The Washington Post in Italy, Turkey, Switzerland and the United States, officials said that nobody except the Soviets appeared to have had an interest in shooting the pope. Vatican sources and some U.S. intelligence analysts following the case have said that grounds exist to suspect a Soviet connection.

But there are wide gaps in the chain of circumstantial evidence that would link Agca to the Kremlin, and the formal inquiry still is in its early stages, according to the correspondents' reports.

"Conducting an investigation is like building a house," Investigating Magistrate Martella told special correspondent Sari Gilbert in his Rome office. "You have to finish the foundation before you can start thinking about the roof."

Martella acknowledged that a Turkish crime boss named Abuzer Ugurlu -- who was named by the media reports as a key link between Agca and the Bulgarians -- was "certainly of interest to the case." The magistrate flew to Turkey to question the "godfather," currently in a prison near Istanbul awaiting trial, where Ugurlu denied any involvement in the attack on the pope.

The media reports contended that Agca had received help before he shot the pope from associates of Ugurlu, who in turn was closely involved with the Bulgarian secret service. The reports maintained that any involvement by the Bulgarian secret service would point to Soviet complicity because Bulgaria is one of the most loyal Soviet satellites and the KGB is said to control the Bulgarian intelligence network.

Turkish intelligence documents also stated that Ugurlu worked closely with the Bulgarian secret service in his smuggling of arms, narcotics and other contraband. The Bulgarians have supplied arms to both far-left and far-right terrorists in Turkey in an apparent effort to promote civil strife and destabilize the NATO country, officials say.

The thesis that the KGB was behind the shooting assumes that the Soviets and Bulgarians worked hand in hand with Ugurlu's crime syndicate and that it in turn was involved with a network of far-right Turkish youths in Western Europe.

Martella declined to say whether he yet suspected any links among Agca, Ugurlu and the Bulgarians and Soviets, adding that he would comment only if he had proof of involvement. He indicated that there was nothing solid to prove at least two of the alleged links between Agca and associates of Ugurlu:

Both NBC and Reader's Digest endorsed Agca's claim that he had obtained his forged passport in Bulgaria. He said that he received it from a Turk who has been described as a member of Ugurlu's gang. When asked about these reports, however, Martella shook his head and said, "How can they say that? They would have to have proof."

When asked about the report by NBC that Italian investigators believed an Ugurlu associate had sent a courier to see Agca on the island resort of Majorca to offer him 3 million German marks and sanctuary in Bulgaria for shooting the pope, Martella said he did not think Agca ever had gone to Majorca.

Summing up his position regarding the media reports, Martella said, "Journalists can afford to make what they see as logical deductions. I can work only on the basis of facts."

The article in the September issue of Reader's Digest was written by Claire Sterling, a journalist and author who has written widely accusing the Kremlin of promoting international terrorism. Sterling also was listed as a contributor to the NBC program, which was aired Sept. 21 and was reported by Marvin Kalb. Both reports acknowledged that the evidence pointing to a Soviet plot was circumstantial and stressed the need for a more intensive investigation of remaining mysteries.

While Martella's probe of Agca's backers seems to have been stymied by a lack of support from other countries, Swiss police have helped him make what apparently is his first big breakthrough in the case.

Acting on Martella's request, police in Olten in northern Switzerland arrested a Turk, Omer Bagci, on June 4 and charged him with supplying Agca with the gun used in the attack on the pope. Swiss officials say Bagci belonged to the Turkish terrorist group called the Gray Wolves, one of several links cited by investigators between Agca and the neofascist group.

Bagci handed the Browning 9-mm automatic to Agca on May 9, or four days before the shooting, according to Martella's extradition request. Italian authorities claim to have recorded a telephone call from Agca in Milan to Bagci in Olten asking for the gun to be delivered, according to a spokesman for the Swiss Justice Department. It was not known why the Italians would have been recording the phone call.

According to the media reports, Agca's gun previously had passed through the hands of a German arms smuggler and Ugurlu associate, Horst Grillmeier. Swiss authorities said that they had no evidence of links between Bagci and either Ugurlu's arms smuggling ring or East Bloc security police.

Investigators believe that somebody was helping Agca between his escape from a Turkish prison on Nov. 25, 1979, and his arrest moments after the attack in St. Peter's Square, because he spent about $50,000 on hotels, transportation and food in his travels during that period without ever taking a job.

Rome's Court of Assizes convicted Agca of shooting the pope and two American tourists standing nearby and sentenced him to life imprisonment on July 22, 1981. In its final report on the case, the jury asked Italian magistrates to hunt down those who had helped the would-be assassin, saying that his act was "the result of a complex plot orchestrated by hidden minds interested in destabilization."

One major enigma in the case is the status of the inquiry into Ugurlu, the Turkish "godfather" and centerpiece of suspicions regarding links to the Bulgarians. He has been in prison for about a year and is scheduled to go on trial Oct. 20 before a court set up only to try smuggling cases. It is unclear whether investigators in Turkey still are pursuing links between him and Agca, and sources close to Turkish police said that he is not likely to be tried on charges related to the shooting of the pope.

The U.S. intelligence source suggested that Turkey has been cautious about revealing information to outsiders in the case, possibly because it prefers to avoid questions about how Agca escaped from a high-security prison--apparently with help -- in November, 1979. West Germany also did not appear to have pursued the case very hard, the source said, possibly because a major question is how Agca could afford to stay in that country for many months without a job.

Martella said that different countries had "different interests" in the case and noted, in an apparent reference to Bulgaria, that it was not worth the trouble to ask some countries for help. He has asked the Justice Department to help him obtain meetings with persons familiar with the case including, possibly, the journalists responsible for the NBC and Reader's Digest articles.

U.S. intelligence sources say that the official assessment in the case does not go beyond strong suspicion that the Bulgarian secret service was involved, although it is widely assumed that if the Bulgarians were involved the KGB would have been behind the Bulgarians.

Both NBC and Reader's Digest quoted only one official on-the-record as directly suggesting Soviet involvement. He was Francesco Mazzola, who was the Italian prime minister's undersecretary for coordination of secret services at the time of the shooting but resigned seven weeks later when the government fell.

When asked about this yesterday, NBC correspondent Kalb told The Washington Post that Mazzola "has got lots of very current information" and "has kept very close touch with what is going on." Mazzola, however said in a telephone interview last week that he has not followed the case closely since he left his post.

Kalb said that other people involved in the investigation for some time also had pointed to Soviet involvement but that he had not included the interviews in the broadcast because of lack of time or the sources' requests for anonymity.

There also has been confusion over NBC's report that the pope sent an envoy to the Kremlin in August 1980 carrying a letter to Soviet President Leonid Brezhnev threatening to "lay down the crown of St. Peter" and return to his homeland if the Soviets moved against Poland. Vatican deputy spokesman the Rev. Pierfranco Pastore issued a partial denial, saying that a letter "with those contents" did not exist but acknowledging indirectly that a message had been sent.

The original transcript of the NBC program, distributed to reporters at a preview screening in Washington on Sept. 14, said that U.S.-born Vatican official Monsignor Hilary Franco had confirmed publicly the role played by the envoy. Reached by telephone that night in Rome, however, Franco said that he had told NBC that there only had been "rumors in the press" about the letter to Brezhnev. Later the same night, apparently after receiving a complaint from Franco, Kalb telephoned The Washington Post to say that he mistakenly had attributed the claim to Franco because of "sloppiness." The attribution was removed in the final broadcast.