Authorities searching for the Rev. Jerzy Popieluszko, kidnaped on Oct. 19, dragged a section of the Vistula River and a reservoir today but reported no sign of the body of the popular priest, now widely feared dead.

A statement by the Internal Affairs Ministry said Popieluszko's alleged abductors, in police custody undergoing questioning since last week, gave conflicting testimony on where they left the 37-year-old cleric.

One of the suspects reportedly said he pushed the priest into the Vistula near Torun, where the kidnaping took place. The other two suspects were said to have pointed to a reservoir near Wloclawek, a town about 30 miles southeast of Torun, as the place where Popieluszko was dropped.

The brief communique did not say which suspect had said what, or whether Popieluszko was reported by the three to be dead or alive when thrown into the water.

Hopes that the outspokenly anticommunist priest may still be alive have faded rapidly since the government announced Saturday that a captain in the Ministry of Internal Affairs had admitted to killing Popieluszko. Two lieutenants in the same department have been named as accomplices in the kidnaping.

Senior communist officials, evidently worried about the damage the incident might do to relations with the Roman Catholic Church and a new labor unrest that it could stir, have condemned the kidnaping in strong terms and promised an intensive investigation. But Internal Affairs Minister Czeslaw Kiszczak complained during the weekend that the suspects were telling differing stories, confusing investigators.

Church leaders and activists of the outlawed Solidarity union are counseling Poles to show calm and restraint pending the outcome of the official inquiry. Calls by isolated groups for work stoppages and prayer meetings at Warsaw's giant steelworks, with which Popieluszko was closely associated, and at the city's FSO auto plant have not drawn much response.

Solidarity founder Lech Walesa, speaking in his home town of Gdansk last night, warned his compatriots against letting themselves be provoked into "bloody revolution." His remarks reflected concern among some opposition leaders that the kidnaping may be part of a larger conspiracy to incite social tensions or part of some kind of internal communist power struggle.

Until it becomes clear who exactly was behind the kidnaping, Walesa and other key activists are trying to avoid an ill-timed confrontation with the state. "We won't let anybody pull us into brawls in which we will lose," Walesa said.

Disclosures about the case have come in stages during the past 10 days, gradually reconciling Poles first to the disappearance of Popieluszko, then to his probable death. The sadness felt by many here is profound. Suspicions linger about which senior party or government officials, if any, may have been backing the kidnapers.

During a Monday night mass attended by 6,000 people at the St. Stanislaw Kostka Church, the Rev. Bronislaw Debkowski called the abduction "a dramatic event of political significance" and warned of further such attacks, United Press International reported.

"The three functionaries of the Ministry of Internal Affairs represented godless hatred," he said. "There is the fear that the same kind of hatred towards the church and priests may exist among other functionaries of the . . . ministry."

Meanwhile, frogmen searching the swirling waters of the Vistula were hampered by the river's strong and tricky current, the government said.

One of the suspects, who was not identified, was taken to the search area to assist in the hunt.