Despite secret diplomatic protests in Washington, Israel has persisted in deploying advanced U.S.-supplied weaponry against Palestinian guerrillas within Lebanon in possible violation of American law, according to knowledgeable sources.

The U.S. arms, which under terms of their transfer to Israel are to be limited to defensive use, have been spotted a half-dozen times by international observers inside Lebanese territory in recent months despite a controversy generated last August by similar deployments, the Arab and Western sources said.

U.S. protests in the past have been followed by Israeli withdrawal of the disputed weapons, which have included heavy artillery, late-model tanks and sophisticated helicopter gunships, the sources said. But the weapons have turned up again on Lebanese soil some time later, they added.

The Carter administration has kept its protests priviate to avoid further friction with Israel, observers here said.

The deployments also are seen as a secondary problem compared to the dispute over Israel's settlements policy and the negotiations among Egypt, Israel and the United States over autonomy for Palestinians in Gaza and the West Bank.

[In Washington, the State Department refused to comment on its diplomatic consultations with Israel, but said that "Israel is well aware of our position" on the arms issue.]

Secretary of State Cyrus Vance said in a letter addressed during the August controversy to Rep. Clement Zablocki (D-Wisc.), chairman of the House Foreign Affairs Committee, that Israel had been told its use in Lebanon of some U.S.-supplied arms may violate U.S. law and the conditions of their transfer.

"Further action on our part will depend on the course of events and our assessment of them," Vance added in the letter, a response to congressmen asking whether U.S. arms control laws had been violated by Israel.

Since then, and as the U.S.-made eapons were again spotted on Lebanese soil, U.S. Ambassador Samuel Lewis in Israel has been instructed a number of times to convey the Carter administration's displeasure in private protests to the government of Prime Minister Menachem Begin, the sources said.

According to Arab analysts here, the weapons have been deployed in Lebanon with increasing frequency in the last few weeks in response to growing number of Palestinian commando raids on villages in the Israel-sponsored "Free Lebanon" border enclave run by Christian militia leader Saad Haddad.

Israeli forces handed over the secessionist border strip, about 60 miles long and five miles deep, as they withdrew under international pressure following their invasion of the border area in the spring of 1978. With Haddad in control instead of U.N forces, the area has become an Israeli-protected buffer separating northern Israel from the bulk of Palestiian guerrillas encamped in the southern Lebanon and headquarters in the town of Nabatiyeh.

Fighting has settled into a sporadic confrontation of limited artillery exchanges and village raids, with an occasional period of several days during which the shelling intensifies. It is during these periods of increased fighting that Haddad's Israeli sponsors bring in the heavy U.S.-made artillery such as 175mm howitzers and self-propelled cannons, Arab sources said.

During the intense shelling of last August, the Israeli 175mm howitzers were used with deadly effect against southern Lebanese villages that Haddad and his Israeli allies said were harboring Palestinian commandos. As a result, a large portion of the south's civilian population fled north to Sidon and Beirut. Since then, most have returned, with occasional temporary fights north during heavy exchanges.

The shelling has drawn little attention in recent months because its intensity is far below that of last August. There are, however, regular exchanges between Palestinian artillery near Nabatiyeh and Haddad's Israeli-supplied howitzers and Sherman tanks in "Free Lebanon" or Israel's own artillery deployed across the border.

In addition, Israeli patrols use U.S.-made helicopter gunships to raid Lebanese villages said to cooperate with the Palestinian guerrillas and to deploy their own U.S.-supplied tanks within the Haddad enclave, the sources said.

Israel made no public commitment to keep its U.S. weapons south of the Lebanon border after the August complaints. But the United States has applied public and private pressure to reduce Israeli shelling and aid to Haddad and to force compliance with the restrictions attached to U.S. arms.