Fighting between pro-Iranian Shiite Moslem forces on one side and pro-Iraqi Palestinians and Lebanese leftists on the other continued to spread in southern and eastern Lebanon today after 15 people reportedly were killed yesterday.

There were reports today of fighting in Burj Rahal and Abbassiya, two villages that so far had not been involved.

Clashes have been reported in at least 10 villages near the southern Lebanese port cities of Sidon and Tyre. Fijian and Irish contingents of the U.N. peace-keeping force had to step in yesterday to separate warring factions near two villages 10 miles north of the Lebanese border with Israel.

Nabih Berri, secretary general of Amal, the Shiite Moslem militia, charged that "joint forces" including Palestinians and leftist-Moslem factions of the National Movement carried out an artillery attack against the Shiite village of Henawiyeh in the south.

Tension gripped Shiite-dominated neighborhoods in and around Beirut as reports of sporadic shooting and explosions in Baalbek and Hermel, in eastern Lebanon, reached the capital. Later a committee of Amal officials and representatives of the joint forces managed to enforce a shaky truce there.

Hostilities between Amal and rival communist and Palestinian factions have killed an estimated 30 people and wounded many more this year. Earlier this month there were violent clashes in areas of Beirut just west of the line separating the city's Christian east and predominantly Moslem western sections.

Shiite sources said the Amal movement, weary of Palestinian activity and the challenge of communist groups vying for control, is bent on cleansing districts it considers its own.

Most southern Lebanese villages are inhabited by Shiites, who make up about a third of the country's population of 3 million. The Shiites, Lebanon's poorest community, have borne the brunt of Israeli incursions aimed at clearing out Palestinian strongholds.

Some southern Shiite families have had to flee their villages several times. Others have migrated north to the capital and live as refugees in vacant apartments, working at menial jobs to survive.

Amal and its followers are ardent supporters of Iran's religious leader, Ayatollah Ruhollah Khomeini, whose Shiite revolution has fueled their fervor and prompted them to assert their identity here. The slaying of Shiite clerics in Iraq and the long war between Iraq and Iran have provoked battles here between Amal and any group associated with Iraqi Baathist ideology or getting financial and military assistance from Baghdad.

Shiite-Palestinian friction has increased lately with the worsening of relations between the Palestine Liberation Organization and Tehran.

While Amal officials insist Iran is not giving them significant help, it is clear that they are strongly influenced by the Tehran government.