Shiite Moslems were close to taking control of the Palestinian refugee camps of Sabra and Shatila today, as they and Palestinians battled on the edges of the city for the sixth straight day today with no truce in sight.

At the Burj al Barajinah camp just north of the Beirut airport, guerrillas fending off Shiite fighters and soldiers from the Lebanese Army fought with machine guns, antitank shells and rocket-propelled grenades.

In Sidon, 25 miles south of the capital, 5,000 angry Palestinians called a one-day general strike and marched in the streets of the Ain Helweh refugee camp, one of Lebanon's largest refugee centers, The Associated Press reported. A counterdemonstration was held in the predominantly Shiite market town of Nabatiyeh in southern Lebanon. Schools were closed and shops shuttered to protest Palestinian shelling of Beirut's Shiite areas during the battle of the camps.

Reports of a Shiite-Palestinian confrontation spreading to the Wavell refugee camp in the Bekaa Valley in central Lebanon reached Beirut. Four persons were said to have been killed in the exchange until Syrian soldiers deployed in the region stepped in to separate the combatants.

News agencies put the number of casualties in Shiite-Palestinian fighting this week at more than 250 dead and 1,300 wounded.

In Beirut, Palestinians who had fled the fighting lay listlessly on the floor of an unfinished underground garage in the Wata al Musseitbeh quarter, waiting for food rations.

Refugees told how their sons were taken away, how some men were lined up against a wall and shot and how Palestinians were left bleeding inside the Dana mosque in the Sabra camp.

One woman, whose two sons in their early twenties were picked up by Shiite Amal fighters combing the neighboring Shatila shantytown looking for guerrillas, said the Shatila mosque was destroyed with wounded Palestinians inside.

"When the muezzin took the loudspeaker to call on Amal to come and collect the casualties, they came in little cars, took their own men away and then destroyed the mosque over the heads of the Palestinians inside," she said. Amal fighters kept reporters from entering Sabra and Shatila, and it was not possible to verify her account.

An Amal fighter at the Sabra vegetable market, now under Shiite control, said the Palestinians defending the camp had "fought ferociously and until death, but we beat them."

Amal leader Nabih Berri offered a cease-fire plan today that was promptly turned down by the National Palestine Salvation Front in Damascus and a Palestinian spokesman here.

The frightened refugees are circulating stories about the execution of Palestinian prisoners. On Thursday, the independent newspaper An Nahar published a picture of a Palestinian with his hands above his head being taken prisoner by Amal gunmen. A picture next to it showed him lying in a heap amid the rubble of a destroyed hut.

Amal spokesmen have denied claims about atrocities.

The Shiite Amal movement is seeking to prevent the return of armed Palestinian activity in Beirut or in southern Lebanon.

Hundreds of families who survived the last week of fighting are now under the protection of the Druze in Beirut. The Druze, who were helped by the Palestinians in fighting Lebanese Christians in 1983, have not tried to stop Palestinian gunners from firing on Shiite positions from Druze-held territory.

Five hundred families were crammed into Wata al Musseitbeh alone, where Abu Mujahed, the secretary of the Popular Committee for the Sabra and Shatila Camps, said all the aid received so far had been from international organizations. No Arab or Palestinian organizations have come forth with any help yet, he said.

Mujahed said he saw Amal gunmen line up and shoot six Palestinian men against the wall of the Dana mosque in Sabra Monday.

"This is worse than 1982," Mujahed complained. "Then there were cease-fires, and the International Red Cross would come in and evacuate the casualties. It is true the Israelis cut off our water supply, but every now and then they would turn it on. Now Amal has blown up our water tanks."