Hundreds of Israeli troops with tanks and armored vehicles crossed into Lebanon today and dug into positions for an apparent extended presence to intercept any Palestinian guerrilla squads headed toward Israel.

Officials in the southern Lebanon headquarters of the U.N. peacekeeping force said more than 300 Israeli troops established three positions about three miles inside Lebanon and began digging trenches and building bunkers and barbed-wire fences.

Today's troop movement, the boldest Israeli incursion into Lebanon in nearly a year, came two days after a Palestinian commando raid on a northern Israeli kibbutz. An Israeli soldier and two Israeli civilians, including a child, were killed in the raid, as were all five Palestinians, members of the Iraqi-backed Arab Liberation Front.

[A State Department spokesman said in Washington that the United States had "sent reports" of the Israeli incursion and was "seeking clarification" from Israeli defense forces.]

The Israeli deployment on Lebanese territory dramatized Jerusalem's lack of faith in the U.N. peacekeeping force's ability or willingness to halt guerrilla infiltration. It also reinforced overt Israeli presence in a swath of southern Lebanon controlled by the Israeli-sponsored militia of Maj. Saad Haddad, a former Lebanese Army officer.

Israeli charged that the Palestinians crossed to their target from southern Lebanon and implied collusion or negligence by U.N, troops.

The armored task force that penetrated the border today thus was seen as a signal of determination that Israeli forces themselves will control Lebanon's side of the border if, as Jerusalem declared, the U.N. forces do not.

Israeli artillery and patrols have regularly but discreetly entered the 60-mile-long buffer zone along the border, despite protests by Lebanon and the United States.The last incursion comparable to today's, however, was a one-day raid in May 1979 shortly after a Palestinian attack in northern Israel similar to Monday's.

The Israeli Army refused to disclose any details of its cross-border operation other than to say that "patrols" were in southern Lebanon "as a precaution against possible terrorist activity," Washington Post correspondent William Claiborne reported from Jerusalem.

U.N. officials said that, in all, at least seven tanks, 25 armored personnel carriers and several bulldozers had crossed the border by nightfall. With them were about 300 Israeli soldiers, they said.

Western observers in the border region said some Israeli units were building roads, stringing barbed-wire barriers and in other ways signaling an intention of remaining in the new positions.

They were centered near the Lebanese villages of Markabe, Kunim, Shaqra and Beit Yahoun, approximately three miles north of the border near areas occupied by Irish and Ghanain battalions of the U.N. force, U.N. officials said.

A pair of armored personnel carriers also pulled up at entrances to the village of Al Tiri, where Irish U.N. troops have clashed with Haddad's militiamen in the last few days, U.N. sources said.

Haddad's men tried to force Irish troops out of the village Sunday night. An Irish soldier was shot in the eye and critically wounded.

The Haddad forces also captured nine Irish soldiers and threatened to execute them unless the U.N. forces pulled out.

After diplomatic contacts, including a demand by the United States that Israel order Haddad to release them, the Irish troops were freed yesterday, but only after another gunbattle in which a second Irish soldier was wounded.

There have been frequent clashes between the 700-man Irish battalion and Haddad's irregulars. The Irish troops occupy an area that protrudes into Haddad's "free Lebanon" enclave and U.N. officials believe he is trying to straighten the "frontier" of his area to ease defending it.

In addition, Haddad has been demanding Irish withdrawal from the U.N. force since Irish Foreign Minister Brian Lenithan recognized the "role of the Palestine Liberation Organization" in any Middle East peace negotiations during a visit to Bahrain in February.

Haddad strongly opposes the PLO and Palestinian presence anywhere in Lebanon. In doing so, he operates as an extension of Israeli policy on the Lebanese side of border.

Wire services reported the following from Tel Aviv:

Israeli troops broke up a Palestinian demonstration in the West Bank today that was a show of support for two of the area's Arab mayors as they were acquitted of charges of assaulting an Israeli policeman.

Israeli television and military spokesman said 40 of the student demonstrators were arrested and about 20 injured in the incident in Ramallah, five miles north of Jerusalem.

The charges against the mayors, Ibrahim Tawil of El Bireh and Kerim Khalaf of Ramallah, stemmed from a scuffle two years ago outside a courtroom where West Bank Arabs were contesting expropriation of their land by Israel. The mayors claimed the charges were politically motivated.