Constantine C. Menges, a senior member of President Reagan's National Security Council staff, told a group of congressional aides yesterday that the Soviet Union "used the Bulgarians to shoot the pope," according to several who attended the on-the-record briefing.

An administration spokesman said Menges recalled speaking only hypothetically, but four of those present said the remark struck them otherwise.

An aide to a prominent Democratic House member said: "It wasn't hypothetical. I was struck by it because it was declarative. I was sitting there wondering if he'd really said that." The aide asked not to be named to avoid antagonizing Menges.

Bruce A. Wright, administrative assistant to Rep. Morris K. Udall (D-Ariz.), said: "It was a casual remark on his part. He made it clear it was his point of view, and I don't think he was trying to represent the administration on it. But he used it as an example of Soviet surrogate activity. I was a little surprised he would make a remark like that in a session on the record."

Menges' comment marked the first time any high administration official had publicly linked the Soviets to the assassination attempt in May 1981 when Pope John Paul II was wounded in Rome. Three Bulgarian government officials were indicted in Italy on charges of conspiring with Mehmet Ali Agca, a Turkish terrorist convicted of the shooting.

The Reagan administration has carefully avoided commenting on published analyses attempting to make a "Bulgarian connection" between Agca and the Soviet Union, long regarded as the true commander of the Bulgarian intelligence service.

Congressional intelligence committee officials said they knew of no information establishing such a link, and State Department spokesman Alan Romberg said the official position on the question had not changed.

Menges, the NSC staff's senior director for Latin American affairs, is known for firmly conservative views and for pushing a hard anticommunist line in administration debates about Central America policy.

He addressed about 75 House and Senate aides invited by M.B. Oglesby, Reagan's special assistant for legislative affairs, to "a special White House briefing on Central America and administration policy" at the Old Executive Office Building.

The remark came in a discussion of the way the Soviets use the troops of nations friendly to them, such as Cuba, to fight democratic forces that Moscow does not wish to engage directly. Congressional aides quoted Menges as saying, "That's why the Soviets used the Bulgarians to shoot the pope." One aide recalled that Menges said "kill," not shoot.

An administration spokesman said Menges recalled saying only that the Soviets, "if they decided to assassinate the pope, would tend to use a partner like the Bulgarians."

Two House aides, also Democrats, said Menges also noted on the record that 15,000 armed rebels are now fighting the leftist government of Nicaragua. Intelligence officials have estimated the number more vaguely at more than 12,000.

In addition, they said, Menges told the group that Cuban President Fidel Castro had played a direct role in the Contadora peace talks through his influence with the Mexican and Colombian governments, which organized the talks along with Panama and Venezuela.

Menges also complained that U.S. media's reporting of various Contadora treaty drafts had focused on Nicaragua's acceptance of one draft rather than three other nations' rejection of it, the aides said.