Lebanese security officials reportedly are hunting for a Shiite fundamentalist sheik with close ties to Iran who is believed to have played a major role in carrying out the suicide bomb attacks on U.S. and French peace-keeping troops Sunday.

The suspect was identified by Lebanese sources as Mohammed Hussein Fadlallah, said to be the leader of the Shiite extremist Hizballah--party of God--which has links to a fundamentalist group in Iran.

According to one report circulating in western intelligence circles, Fadlallah was in the Shiite suburb adjacent to the U.S. Marine compound the night before the attacks and gave his final blessings to the two men who volunteered for the suicide mission of driving the trucks loaded with explosives.

Despite mounting indications of involvement by pro-Iranian Shiite extremists in the execution of the bombing, most circumstantial evidence about who masterminded it points toward Damascus.

But outsiders note that much of the information being leaked to the press here or circulating in diplomatic circles appears to come from the intelligence service of the Christian Phalangist Party. It has an especially strong interest in implicating the Syrians because it holds them responsible for the assassination of the Phalangist leader, president-elect Bashir Gemayel, in September 1982.

Because of the publicly known close ties between the Lebanese fundamentalist groups and Syria, observers say, there is good reason to believe the Syrians were aware of the operation, sanctioned it and possibly aided in organizing it.

But seldom has the full truth emerged about who was behind any major Lebanese assassination or bomb explosion, including the bombing at the U.S. Embassy here last April that killed more than 60 people and one at the Iraqi Embassy in 1981.

It is nonetheless widely believed among Lebanese and in western and Arab diplomatic circles here that no operation of such enormous implications and far-reaching consequences as the bombing of buildings housing hundreds of U.S. and French soldiers could take place here without Syria at least approving of it in advance.

The Syrians had previously occupied both buildings destroyed in the explosions and thus had an intimate knowledge of their layout, construction and stress points.

Syrian intelligence chief Mohammed Ghanem had his offices in the eight-story French Army building before the Israeli invasion of June 1982. Many of the buildings now housing French Army units throughout Beirut were formerly used by Syrians or security forces of the Syrian-organized Palestine Liberation Army, giving Syria an intimate familiarity with them.

The Syrians are the protectors of the two Shiite fundamentalist groups that American and Lebanese officials suspect as likely executors of the Sunday bomb attacks--Hizballah and the Islamic Amal, a breakaway faction of the main Shiite Amal movement.

Both groups are based in Baalbek in the eastern Bekaa Valley, well behind Syrian lines in Lebanon and under Syrian control. With Syrian blessing, Islamic Amal, under the leadership of Hussein Mussawi, has set up a symbolic Iran-style "Islamic republic" in Baalbek.

Mussawi, 42, once a schoolteacher, is the man most mentioned in Washington as organizer of the attacks. He appears to command the contingent of 300 to 500 Iranian Revolutionary Guards that Ayatollah Ruhollah Khomeini sent to Lebanon in the summer of 1982 to help the Palestinians fight the invading Israeli Army.

In a meeting with western journalists in Baalbek today, Mussawi denied responsibility for Sunday's attacks but he said, "I salute this good act and I consider it a good deed and a legitimate right and I bow to the spirits of the martyrs."

He said he hoped to cooperate with such operations in the future.

Mussawi is known as a fervent believer in Iran's Islamic revolution.

His Islamic Amal has nothing to do with the rival Amal movement in the Beirut area under the leadership of Nabih Berri, who is married to an American and is a frequent visitor to the United States.

Mussawi once headed the military wing of Berri's Amal and was his second in command but he split off to form his own group in the late 1970s, condemning Berri as too "moderate."

The Phalangist Party has been particularly active in implicating Mussawi in the attacks. Today's edition of the French-language L'Orient le Jour, for example, published a report from the party's press that alleged Mussawi had set up a "terrorist camp" at his home village near Baalbek under the guise of a center for "scouts of the Islamic mission."

The Phalangist report said there were 150 youths undergoing training in terrorist tactics there under Syrian instructors. Later they were sent for advanced training to a camp near Damascus, it said.

It said a Syrian-supervised ring had been operating in the Bekaa to steal cars and trucks, change the license plates and motor numbers and send them back to Beirut, apparently to serve as car and truck bombs. The operation was carried out, it said, in collaboration with Hizballah.

Far less is known about Hizballah, but knowledgeable Lebanese sources said it was composed of a few hardcore fundamentalists and linked with an Iranian group known as Hizbdawa.

Lebanese security knows so little about its leader, Fadlallah, that it has been searching libraries of local newspapers for photographs of him.

Followers of Hizballah began infiltrating the southern suburbs of Beirut in small numbers starting in August and have been accused of provoking incidents with the U.S. Marines during last month's heavy fighting here. Berri has worked with only partial success to bring them under his control and has not been able to move them out of his area.

It is unclear how closely Fadlallah and Mussawi work together. But the bomb truck drivers to whom Fadlallah reportedly gave his blessing were said to have been provided by Mussawi's Islamic Amal.

If Fadlallah was in the Beirut area Saturday night, it is considered likely that he fled immediately to Baalbek, where he would now be out of reach of the Lebanese.

The Phalangist Voice of Lebanon radio warned Saturday night, on the eve of the attacks, that Syrian intelligence operatives were infiltrating the southern suburbs, with some staying at unnamed "foreign embassies." Sunday, after the bombings, it named the Iranian Embassy.

There has been no independent confirmation of these reports. But one high official of Berri's Amal told a Lebanese reporter this week that Syrian and Palestinian agents had been arriving in the southern suburbs in small numbers.