Red Brigades terrorists killed a respected Italian economist and trade union official here today, raising concern that the left-wing group might be beginning a new campaign of violence after more than a year's silence.

It was the first Red Brigades slaying here since the assassination on Feb. 15, 1984, of Leamon Hunt, the American director of the Rome-based Sinai Multinational Force.

Ezio Tarantelli, 43, professor of political economy at Rome University, was machine-gunned to death this morning in a parking lot outside a university lecture building by two young men who escaped on a motor scooter. Tarantelli was also head of the research institute of the Catholic-Socialist trade union CISL, Italy's second largest.

Tarantelli, who was married to an American, was shot 12 times, police said, and was pronounced dead on arrival at a Rome hospital.

Later in the day, an anonymous caller to a Rome radio station claimed responsibility for the killing in the name of the Red Brigades. Rome police also said a copy of a recent, 25-page Red Brigades ideological document on Italian labor conditions that was signed "Communist Fighting Party-Red Brigades" also had been found on the ground near Tarantelli's car.

The slaying of Tantarelli, a former researcher and lecturer at Massachusetts Institute of Technology, was the first Red Brigades attack against an Italian in two years and sent shock waves through a country.

"The insane fragments of terrorist fanaticism once again have killed a just man," said Italy's Socialist prime minister, Bettino Craxi. "Ignorance has donned the macabre garments of the assassin."

The Red Brigades had come close to disintegrating after the successful rescue of a kidnaped U.S. general in January 1982 and the arrest of his captors.

But Craxi told parliament in February that intelligence reports indicated that a new terrorist attack was to be expected, probably in Rome.

Police here believe that about 50 of the left-wing terrorists still sought are probably in the capital and say that an apparent conflict in the terrorist group between hard-liners and moderates has ended with the hard-liners as victors.

When Craxi made his prediction in parliament, many European countries were plagued by anti-NATO and anti-U.S. terrorist acts. But today's killing seems more in line with the Red Brigades' traditional tactic of generally choosing victims because of their symbolic value to Italy.

Tantarelli was involved in discussions regarding the controversial Italian wage indexation system, revisions of which are now scheduled to be tested in a referendum later this spring.

The attack came only three days after Italian police in Padua killed two right-wing terrorists and wounded two others when the four began firing from their car after being stopped at a police roadblock.

The Sunday shoot-out involving right-wing terrorists created a stir here because all of the four involved were 22 years of age or less, indicating that the rhetoric of political violence is still attractive to some segments of Italian youth.