BEIRUT, Lebanon (AP) _ Rival Shiite Moslem factions agreed to begin a cease-fire Wednesday and withdraw forces, but past truces quickly collapsed and some officials wonder how much control the warlords are willing to relinquish.

Police reported the cease-fire between the pro-Iranian Hezbollah, or Party of God, and the Syrian-backed Amal movement began at midnight. Their three- year battle has killed at least 1,100 since June 1987, police estimate.

A joint communique indicated they expect further meetings to discuss a possible prisoner exchange pending ''a comprehensive and final settlement under the auspices of Syria and Iran.''

The Moslem Voice of the Nation radio said Iranian Foreign Minister Ali Akbar Velayati was due in the Syrian capital of Damascus this week to work on ''an agreement putting an end to the Amal-Hezbollah dispute.''

The pact bolstered President Elias Hrawi's efforts to implement an Arab League-brokered peace plan to end Lebanon's 15-year-old civil war, which has claimed more than 150,000 lives.

The government said efforts to demilitarize Beirut and surrounding hills is ''progressing quickly.''

There have been dozens of failed cease-fires in the feud for control of Lebanon's 1.2 million Shiites, the country's largest sect.

The present cease-fire was called after meetings between senior leaders of the two factions. The talks in Anjar, east of Beirut, were attended by Brig. Gen. Ghazi Kenaan, Syria's military intelligence chief in Lebanon, and Iran's Ambassador to Syria, Mohammad Akhtari.

Hezbollah, which is blamed for many terrorist attacks, is considered to be the umbrella organization for extremist groups holding foreign hostages in Lebanon, including six Americans.

A police spokesman, who cannot be named under standing regulations, said fighters of both factions still hold their positions in south Lebanon, where some of the worst clashes took place.

''We don't expect them to withdraw unless Syria and Iran succeed in working out a political settlement to the conflict,'' the spokesman said.

Hezbollah and Amal say they will withdraw fighters from a 15-mile coastal strip that includes Beirut.

Agriculture Minister Mohsen Dalloul announced earlier Wednesday that the right-wing Christian Lebanese Forces militia, led by Samir Geagea, also agreed to withdraw from the war-battered capital.

The other main militia, the Druse Moslem Progressive Socialist Party led by Walid Jumblatt, has also consented to pull out of the city.

''We break the good news to the Lebanese people, who are longing for peace,'' Dalloul announced after a five-hour meeting with Geagea and Defense Minister Albert Mansour.

Dalloul, a Shiite, and Defense Minister Albert Mansour, a Greek Orthodox Catholic, have been assigned by the government to negotiate the militia withdrawal.

The government has not yet set a deadline for the withdrawal, but Hrawi is expected to press for it as soon as possible.

Hrawi announced the plan after the Syrian army and Lebanese troops crushed rebel Christian Gen. Michel Aoun's forces in an eight-hour offensive Oct. 13.

More than 500 people, including about 200 Syrian soldiers, were killed and 1,200 wounded.

The collapse of Aoun, who fled to refuge in the French Embassy, removed a major obstacle to the peace plan Hrawi was elected last November to implement.

Aoun opposed the accord because it did not guarantee a complete withdrawal by Syria's 40,000 troops in Lebanon, who he considered an army of occupation. Aoun and Hrawi are Maronite Catholics, who have dominated Lebaneses politics since the nation's independence from France in 1943.

The Syrians have said they will pull out of Beirut and other cities to the Bekaa Valley in eastern Lebanon within six months of the plan being implemented.

But many believe other rival commanders fear making the first move to withdraw and leave their forces exposed to attack.

Geagea, for instance, faces threats from Syrian-backed Christians.

Jumblatt, whose 200,000-member Druse sect if one of the smallest in Lebanon, has been critical of Hrawi's government and has vowed to keep government authority from extending to his stronghold in the Chouf Mountains southeast of Beirut.