The Islamic Jihad Organization, a little-known terrorist group that has claimed responsibility for the explosion at the American Embassy in Beirut and for attacks on French and Italian targets there, is seen by U.S. sources as a strong supporter of the Iranian government of Ayatollah Ruhollah Khomeini, if not actually linked to it.

Beyond telephone calls purportedly made in behalf of the organization, however, there is no evidence of its existence or makeup, U.S. sources in Beirut said.

Although a caller to a Beirut newspaper Monday said Jihad had bombed the U.S. Embassy as "part of the Iranian revolution's campaign against imperialist targets," the Iranian government, as it has in the past, denied any involvement with the group.

Iranian Foreign Minister Ali Kabra Velayiati, in a statement published by Iran's news agency, said, "We deny any involvement and we think this allegation is another propaganda plot against us."

Islamic Jihad (which means Moslem holy war) was first heard of when an anonymous caller claimed responsibility on its behalf for a similar car-bomb explosion at the French Embassy in Beirut on May 24, 1982. That explosion killed 12 people and wounded 27.

Similar calls claimed responsibility for grenade and machine-gun attacks on U.S. and Italian soldiers of the multinational peace-keeping force on March 16, 17 and 18, that killed one Italian and wounded eight Italians and five Americans. On April 9, a similar call followed gunshots at French peace-keeping forces that caused no casualties.

There are indications, but no proof, that Jihad is linked with the Islamic Amal force, breakaway members of the Amal militia, a Shiite Moslem force in Lebanon. The Islamic Amal force is based in and around Baalbek, a Lebanese town under Syrian control 45 miles east of Beirut where several hundred Iranian Revolutionary Guards have taken up residence.

The Islamic Amal militia seized control of Baalbek's city hall Nov. 22, Lebanon's national day and unsuccessfully attacked a Lebanese Army barracks there. Lebanese authorities blame Islamic Amal for an attack in March that killed six Lebanese soldiers.

Last month, a large wall inscription in central Baalbek, near posters of Khomeini, proclaimed, "Death to the Americans, death to Israel, death to the Russians."