Israeli soldiers scouring the occupied Lebanese countryside have rounded up between 5,000 and 6,000 Palestinians and are holding them in internment camps in Lebanon and Israel.

With Israeli prisons already overcrowded and Israel refusing to grant prisoner of war status to captives whose only provable offense may be membership in the Palestine Liberation Organization, Israeli officials acknowledge that there are awkward questions to be faced in the future.

But for now, manhunts and interrogations are continuing throughout the occupied southern part of Lebanon, and the number of Palestinian prisoners in the makeshift camps is likely to rise in the weeks ahead.

Several dozen prisoners, some of them blindfolded, were seen being questioned by Israeli soldiers carrying switches at a fruit-packing plant just south of Sidon. A knot of women waited across the road--forced away from the iron gate by an Israeli trooper--seeking word of their husbands or sons taken into custody.

"There is God," shouted one woman in Arabic as she was being gently pushed back by an Israeli border policeman. "There is God. There is God."

"God is for all of us," replied the trooper, also in Arabic, forcing her to retreat.

The wife of Talal Hayeh said he was arrested without explanation after an Israeli truck with a loudspeaker drove down his street in Sidon and ordered all men to surrender a week after the last fighting here. Hayeh, a 35-year-old Palestinian, was a schoolteacher at the U.N. Relief and Works Agency school at Ein Hilweh camp here, his wife said, and "he was into nothing else; he was clean."

Lebanese residents of Sidon said many of their relatives also have been arrested and have not been heard from since. One shopkeeper complained that because of the large number of Lebanese arrested on suspicion of cooperating with Palestinian guerrillas, the city's commerce remains hobbled, with many shop owners still in detention.

Although most Lebanese are expected to be released once their identity is established, Prime Minister Menachem Begin's government has left the fate of captured Palestinian guerrillas unclear. Israeli officials say the Palestinians will not receive prisoner of war status under the Geneva Conventions, saying they fail to meet a convention requirement that "the conduct of their operations is in accordance with laws and customs of war." For the time being, they are being held under emergency ordinances that allow the Army command to renew their detention without trial every three months.

The number of Palestinian prisoners reported by the Israeli command is a measure of the crushing blow dealt the guerrilla movement by the invasion. According to reliable estimates, the Palestine Liberation Organization fielded about 16,000 full-time guerrillas before the conflict began. In addition to the 5,000 to 6,000 prisoners, Israeli officials say they have killed 2,000 guerrillas, meaning about half the main PLO force has been eliminated, according to Israeli counts.

An Israeli Foreign Ministry spokesman said government legal experts are studying what status the captured Palestinians should receive. In the meantime, he added, they will receive the same kind of treatment they would if they were accorded POW status as defined by the 1947 Geneva Conventions.

Eventually, some may be brought to trial under an Israeli law that allows the government to prosecute PLO members--even if they joined outside Israel--as members of a hostile organization. Justice Minister Moshe Nissim has appointed two special tribunals to weigh the question.

From time to time in the past, Israeli Army units have crossed into Lebanon and captured suspected guerrillas, bringing them back to Israel for trial under this law. Also, in the late 1960s and early 1970s, the Army would pursue guerrillas who had infiltrated from Jordan across the border and capture them. Israeli authorities decline to say how many people have been prosecuted as PLO members from outside Israel.

As the roundup continues, the Palestinians are being held in at least two internment camps, one near Sidon and the other just south of the Israeli border with Lebanon.

An Israeli reporter who visited a camp near Sidon said the prisoners were divided into three categories: Lebanese, who were freed after establishing their identities; Palestinians who could prove they were civilians, and Palestinian guerrillas who took part in the fighting or were alleged to be PLO members.

The captured guerrillas are likely to remain in camps until their fate is decided. Authorities said that even before the invasion Israeli prisons were overcrowded with 6,500 prisoners, comprising about 3,000 Palestinians convicted of acting against Israel and another 3,500 Israelis jailed for a variety of crimes.

Several delicate considerations surround the prisoners being rounded up now. Israelis are sensitive to world public opinion, and the presence of thousands of Palestinians in internment camps creates a distasteful image, particularly for a country in which many of its citizens were in World War II concentration camps. The Israeli Army command also believes some of the 23 Israelis missing in action are being held prisoner by the PLO and could be subjected to retaliation.

The PLO has announced the capture of only one Israeli, a Skyhawk pilot whose plane was shot down June 6.