Italian judicial officials in the port city of Genoa today issued warrants for the arrest of 20 Arabs who they claim belong to a vast and previously unknown Arab terrorist group headed by a mysterious Palestinian they believe to be living in London.

The terrorist network, according to judicial officials, was discovered through the interrogation over the last 40 days of a Jordanian-born Palestinian named Awni Hindawi, who was arrested here last June.

Hindawi, 24, is a cousin of the two brothers of the same name now under arrest in London and West Berlin for the failed attempt to plant concealed explosives aboard an Israeli airlines flight from London to Tel Aviv and the bombing of the La Belle disco in West Berlin.

The Italian action today was the latest result of a half-dozen investigations into elements of Arab terrorism that have used, or sought to use, Italy as a base of operations in Western Europe in the past year.

It comes on the heels of the successful prosecution in Italy of 14 persons involved in last fall's hijacking of the Italian cruise liner Achille Lauro during which an elderly, wheelchair-bound American, Leon Klinghoffer, was slain. Other Italian magistrates are investigating Libyan connections to terrorist activities in this country, various unresolved terrorist bombings in Rome last fall and the simultaneous terrorist attacks on the Rome and Vienna airports last December.

In announcing the issuing of the arrest warrants today, investigating magistrate Luigi Carli gave out no names but said that interrogations of Hindawi had revealed the existence of a new, "complex and extended organization with links to international terrorism." He said the 20 persons being sought were all charged with belonging to an armed terrorist band, a crime under Italy's aniterrorist laws.

The Genoa magistrate, who last month prosecuted the hijackers of the Achille Lauro, maintained silence about the identities of the 20 and what they are alleged to have done. But sources close to the investigation said the warrants involve a group of Arabs in various countries in West Europe, including Hindawi, who for the past five years had been a student at Genoa University.

These judicial sources said that of the 20 persons sought, 11 were already under detention or had been arrested in recent days -- seven in Italy, three in West Berlin and one in London.

Carli told reporters that there seemed to be no links between the new organization and the Palestine Liberation Front headed by Mohammed Abbas, who was convicted in absentia earlier this month of organizing the Achille Lauro hijacking and sentenced to life imprisonment.

Three of the ship's four hijackers, including the confessed slayer of Klinghoffer, received sentences ranging from 15 to 30 years while the fourth, a minor at the time, is still to be tried in juvenile court.

But Carli indicated that there was some evidence that the new group had links with the terrorist organization headed by Palestinian renegade Abu Nidal, said to be the mastermind and organizer of the Vienna and Rome airport attacks.

Although conclusive evidence has yet to emerge, intelligence officials investigating the two Hindawi brothers' links to the London and Berlin terrorist actions last April have indicated that they believe they were either "sleeper" agents in Europe for Abu Nidal or were hired by his terrorist organization to conduct the attacks.

Nezar Hindawi is currently charged and under arrest in London in connection with the attempted El Al bombing.

A notebook found in his possession led police in West Berlin to investigate a Palestinian living there under the name of Ahmed Hazi, who was discovered to be Nezar Hindawi's brother and linked to the April 5 bombing of the La Belle disco. Two persons, including a U.S. serviceman, died in the attack, and 175 others were wounded.

President Reagan cited alleged evidence that Libya had been behind the two attacks as justification for his decision to bomb Tripoli and Benghazi, Libya's most important cities, April 15.

Libya's Col. Moammar Gadhafi is believed by Western intelligence agencies to be a major supporter of Abu Nidal, who uses Libya and Syria as bases of operation.

Awni Hindawi, in turn, was discovered in Genoa because of Ahmed Hazi's interrogation in West Berlin.

How close Awni Hindawi's links were to his two Jordanian-born Palestinian cousins remains unclear. Italian judicial sources said that he has sought to disassociate himself from the London and West Berlin incidents, but added that evidence points to the possibility of his having been used to support them without knowing the details of his cousins' plans.

Awni Hindawi has been described here by judicial sources as quiet and introverted. But his passport also showed that he traveled frequently to Syria and Jordan during his long stay as a student of political science in Genoa.

Hindawi has also been linked to another Jordanian-born Palestinian in Italy, Adnan Roussan, 40, who has headed a large textile import-export firm based in the Italian city of Verona. Roussan, who intelligence officials here suspect of using his business as a cover for arms trafficking, was one of the seven arrested in Italy under today's warrants.