BEIRUT, Lebanon (AP) _ Gunmen shot and killed a Christian doctor in Moslem west Beirut Tuesday, despite government efforts to end lawless militia rule.

Police said two gunmen burst into a clinic run by Dr. Zahi Hawa, a leading gynecologist, and shot him several times before fleeing.

Hawa died later at American University Hospital. Police said they knew of no motive for the attack.

Moslem extremists have been terrorizing Christian families in west Beirut for months. Scores have been been kidnapped, and hundreds of families have left the country or fled to Christian east Beirut.

Christians geneally coexisted peacefully with the Moslem majority in west Beirut before the civil war erupted in 1975.

But leaders of the dwindling Christian community estimated that only one- quarter of the 200,000 Christians who lived in the sector before 1975 now remain.

The violence underlined the problems facing an 850-man joint police-army task force deployed last week to try to impose law and order.

The Moslem half of the capital, with a population of about a half-million, has been gripped by anarchy since militias drove out Christian units of the army in March 1984.

The task force has patrolled the streets in armored vehicles since rival Moslem factions fought for five days last month for control of west Beirut, killing 68 people and wounding 300.

Militia leaders ordered their men to lay down their guns, but the task force has been unable to quell West Beirut's endemic violence.

Two Christian Lebanese freelance employees of NBC News, cameraman Melhelm Hnein, 36, and driver Yussef Awwad, 62, were feared kidnapped, the television network reported.

The men disappeared Monday as they drove from east Beirut to work in the Moslem west side, a member of NBC's Beirut bureau said. He asked not to be identified.

''We fear they've been kidnapped, but we have not had any contact from any faction yet,'' he said.

Mary Lou O'Callaghan, director of news information at NBC in New York, said: ''No NBC news employee was with them. NBC has nothing more to say except to confirm they are missing and we are looking for them.''

In another abduction, a statement purportedly issued by the Organization of the Oppressed on Earth said four kidnapped Jews would be killed if Israel does not free about 300 Shiite Moslems the group claims are held in Khiam prison camp in south Lebanon.

The camp is believed to be run by an Israeli-backed militia, the mainly Christian South Lebanon Army.

''We shall begin executing (the kidnapped Jews) unless the strugglers in Khiam are released soon,'' said the statement published in the leftist As- Safir and independent An-Nahar dailies.

The group, believed to consist of Shiite zealots seeking to create an Iranian-style Islamic republic in Lebanon, did not set any deadline for killing the four men, identified as Isaac Sasson, Isaac Tarrab, Elie Srour and Chaim Cohen Halala.

The statement claimed that the men, who were kidnapped nine months ago, are ''spies attached to the Israeli secret service.''

Sasson, 65, is head of west Beirut's tiny Jewish community, said the police.

On the Green Line dividing Christian east Beirut from the Moslem west side, Moslem gunmen battled Christian militiamen with rocket-propelled grenades. Police did not report any casualties.