Israeli troops invaded southern Lebanon last night, apparently in large numbers and with air and naval support, in a declared effort to "clean out terrorist bases."

There was no immediate indication of the size of the operation, which was announced by Israeli military officials in Tel Aviv and confirmed by reports from Lebanon. But authoritative sources said it included thousands of troops and a U.S. official here described it as "an extensive attack."

The invasion was clearly in retaliation for the Palestinian terrorist attack in Israel on Saturday that resulted in the death of 36 Israelis and nine of the 11 commandos who took part in the raid.

Shortly before launching the invasion, Israel buried 12 more victims of the Saturday attack and Education Minister Zeveluu Hammer declared at the funeral that Israel would fight the Palestine Liberation Organization until "they are destroyed."

By late last night it appeared that Israeli forces had not moved north of the Litani River, 10 miles above the Israeli-Lebanese border. Syria's peace-keeping troops in lebanon are situated north of the Litani and any Israeli penetration of that area could escalate the retaliatory raid into a full-fledged confrontation with Syria.

Because of censorship from Israel and difficult communications with southern Lebanon, it was virtually impossible to learn the numbers of troops involved and the exact area of their operations.

Washington Post correspondent Jonathan C. Randal reported from Beirut that PLO sources there said Israeli aircraft were attacking Bint Jbail, a long-standing Palestinian guerrilla stronghold, and an Israeli armored force was moving toward Rmaich, across the border from the Israeli town of Metullah.

Israeli aircraft were flying over Tyre and Sidon on the Mediterranean coast, the PLO said, and Israeli naval vessels were off both ports but had not fired.

The Israeli army said in a communique that the strike into southern Lebanon was intended "to root out the terrorist bases near the border and to strike at their special bases from which terrorists set out on missions deep inside Israeli territory."

The military spokesman said Israel did not intend "to harm the population, the Lebanese army or the [Syrian peacekeeping] force, but only the terrorists and their helpers."

The purpose of the invasion, he said, was "to safeguard the lives and security of the population of Israel."

The State Department urged Monday that any retaliation avoid the loss of "innocent lives" and yesterday Lebanese Foreign Minister Fuad Butros called in U.S. Ambassador Richard Parker in Beirut to plead with him for U.S. support in preventing "any danger that befall Lebanon and the Lebanese people."

In New York, Zehdi Terrzi, the PLO's permanent observer to the United Nations, warned that the Israeli invasion "might escalate into a full-scale war."

But Israeli troops have moved into southern Lebanon in the past with the same declared purpose, and pulled out within a few days.

Through much of last year, Israeli troops moved virtually at will in much of southern Lebanon, giving assistance to Lebanese Christians who were fighting Lebanese leftists and Palestinians in an offshoot of the Lebanese civil war.

Israeli troops withdrew from Lebanon in September on the basis of a cease-fire negotiated with the assistance of U.S. diplomats in Beirut.

Under the cease-fire, Palestinian commandos were to pull back from the Israeli border. Both sides have accused each other of violating the terms of the agreement, however.

Southern Lebanon has been a base for Palestinian attacks against Israel for years. israeli villages along the Lebanese border, such as Metullah. Maalot and Kiryat Shemona have been victims of bloody attacks, most of them followed by Israeli reprisal raids.

Many large Palestinian refugee camps, most of them with commando forces, are in the area, especially in the region of the coastal cities, Tyre and Dison.

The Israeli reprisal could become yet another in a fast forgotten series over the past decade if Israel limits, its retribution to the 10-mile deep area between its border with Lebanon and the Litani River.

At Israeli insistence that area has been off limits to Syrian troops since 1976 when Syrian President Hafez Assad began sending troops into Lebanon to stop the civil war.

Since Israel forbade Syrian troops south of a never officially defined "red line" - presumed to run more or less north of the Litani River - then Assad's prestige is not in question if the reprisals are limited to that area, diplomats reason.

There are grave doubts that Syria could afford to look the other way if Israel hits Palestinian refugee camps or other targets in the rest of Lebanon where Syria's 30,000-man peacekeeping force is supposed to be in charge.

Theoretically at least under terms of December's Tripoli summit conference of countries opposed to Egypt's go-it-alone diplomacy with Israel, an attack on any of the signatories - Algeria, Libya, the Palestinians, South Yemen and Syria - was to be considered as an attack on them all.

If Syria did nothing if Israeli forces cross the river it would run the risk, paper tiger, the fate that befell the Lebanese army even before its civil war disintegration.

If Syria were to fight back, Israel would be provided with a pretext for disposing of the only Arab army that counts now that Egypt has taken itself out of the Arab order of battle.

Those who see the decrepit state of Syrian equipment in Lebanon - some estimates claim between 50 and 75 per cent of its armor is out of order at any one time - or look at its overextended logistical system may question Israeli descriptions of Syrian armed might.

Despite the tough talk from Damascus, observers are convinced that Assad entertains few illusions about his chances of surviving if Israel were to seek to engage his forces in Lebanon in a major clash.

Although last month's fighting between Lebanese and the Syrian army here chastened some of the more extremist rightwing Christian elements in the Lebanese army and private militia, there are real fears that they could seek to embroil Syria in just such a confrontation.

Their goal apparently would be to push south to link up with Israeli forces moving north - a joint operation designed both to smash the Palestinian guerrillas and split the Syrian army.

Israel perpetuated the no-man's-land status of the deep south last September when it vetoed security arrangements laboriously worked out by Syria, Lebanon, and the Palestinian guerrillas.

The guerrillas were to have withdrawn from the border area - a longstanding demand by previous Israeli governments - and been replaced by fledgling units of the new Lebanese army emerging from the ashes of its civil war anarchy.

Israel preferred to maintain instability in the deep south, in the view of the Arabs.

At times its American-manufactured heavy artillery has helped drive as many as 100,000 Lebanese civilians from their homes. At others Israel has aided Christian militiamen in their fight against the Palestinians and their Lebanese leftwing allies.