Palestinian spokesmen claimed today to have inflicted major casualties on what they said were "25,000 invaders" who crossed southern Lebanon from Israel this morning and to have destroyed 42 armored vehicles and shot down two fighter-bombers and two helicopters.

As Israeli troops moved in three prongs northward across the border, the Lebanese government held an emergency session and decided to ask for an immediate summit meeting of the 22-nation Arab League.

Hours after the fighting began, a Syrian military spokesman in Damascus said Syrian troops in southern Lebanon had "come into contact with" Israeli units in three locations on the east-central part of the border. The spokesman said Syrian troops, part of the 23,000-man Arab Deterrent Force sent to Lebanon in 1976 to police the aftermath of the 1975-76 Lebanese civil war, had been "ordered to oppose" the Israelis and "were doing so."

The wording of the communique suggested to analysts that the Syrians were not engaged in actual fighting, and there was no confirmation of the Syrian announcement from their formal Palestinian allies. The Syrians were not involved in Israel's previous invasion of Lebanon in 1978, and an Israeli statement announcing the invasion today pointedly said Syrian forces would not be attacked if they did not intervene.

Tonight, however, the state-run Radio Lebanon said that Syrians had been involved in mounting heavy artillery against Israeli positions today.

The Israeli attack pushed aside troops of the United Nations buffer zone that has divided the two countries since 1978. A spokesman for the United Nations peace-keeping force headquarters in Naqurah, on the Mediterranean coast just north of the Lebanese-Israeli border, said that an Israeli armored brigade had reached Baas refugee camp at the Mediterranean port of Tyre, about five miles south of the Litani River.

Other Israeli units, apparently from a second armored brigade, were reported by the Palestinian news agency WAFA to have reached the outskirts of Nabatiyah, the main Palestinian stronghold north of the Litani.

Nabatiyah, the most important single Palestinian-held position because it commands a full view of northern Israel, has been under periodic Israeli air attack for years.

Both the United Nations and WAFA reported heavy Israeli air strikes against Palestinian positions at the nearby ruins of the Crusader castle at Beaufort. Other major air strikes were reported on the town of Sidon, north of the Zahrani River and about 25 miles south of Beirut.

Washington Post correspondent William Claiborne reported from Israel early Monday that Israel had claimed to have captured the castle.

Although Palestinian and leftist Lebanese antiaircraft guns fired throughout most of the day in Beirut, there were no attacks against Beirut, which was hit with waves of Israeli bombers Friday in which at least 210 persons were killed and 500 wounded, according to Palestinian and Lebanese officials.

Although the Palestinians claimed by nightfall to have inflicted "more than 200 casualties" on the Israelis, estimates of Palestinian and Lebanese casualties in today's widespread fighting were not immediately available. The Israelis confirmed that one of their planes had been shot down by the Palestinians. Downed Skyhawk pilot Ahiaz Aharon appeared at a Beirut news conference organized by the Palestine Liberation Organization.

In the extreme east of the 33-mile-long front, a Norwegian soldier serving with the 7,000-man U.N. force was killed by shrapnel, although conflicting accounts held that he was caught in Palestinian-Israeli cross fire or hit as his unit sought to stem the Israeli advance.

Along the north-south coastal highway, the westernmost Israeli brigade pushed through a Dutch-held U.N. roadblock two miles south of Tyre, but heavy fighting was reported by both the United Nations and WAFA as the invaders approached the ancient Phoenician city.

The Palestinians also reported an Israeli helicoper-borne assault north of Tyre and a naval raid against the fortified Palestinian camp at Rashidiyeh just to its south.

In the central sector, according to the United Nations, another Israeli armored brigade moved out of Taibe in territory held by Lebanese Christian Maj. Saad Haddad, an Israeli ally, and crossed the French battalion's sector. The invaders then threw pontoon bridges across the Litani River at Kakaiet. That force was thought to be closing on Nabatiyah.

In the east, Israeli armor and infantry advanced along a road constructed on the slopes of Mount Hermon in the Norwegian sector of the U.N. zone and then turned west.

On the Mediterranean coast, a seaborne and helicopter-borne Israeli assault was reported near Zahrani where one of the county's two refineries was damaged. A Lebanese government source said at least one storage tank was set on fire and in Beirut almost immediately long lines formed outside gas stations.

The Palestinians claimed they had repulsed that attack but other sources suggested that the Israelis had interrupted traffic not only along the north-south coastal highway but also had seized the road juction on the paved road leading east ot Nabatiyah.

Meanwhile, Palestinian sources reported Israeli helicopter-borne troops and armor were progressing toward Nabatiyah from east, south and west.

But so devastating has been Israeli bombing that all major roads in southern Lebanon have been cut and independent confirmation of the belligerents' claims made impossible.

As with the 1978 Israeli invasion of southern Lebanon, which did not go beyond the Litani, there was little Arab reaction to the assault, and Radio Lebanon spoke of "a stunning silence" from the Arab world.