Prime Minister Menachem Begin, speaking in parliament where his government today easily defeated a no-confidence motion over the invasion of Lebanon, warned Syria not to engage Israeli forces as they continue their attacks on Palestinian positions.

The prime minister urged Syria not to interfere with the Israeli Army's attempts to create an "artillery-free" zone in areas of southern Lebanon that have been held by the Palestine Liberation Organization. Yet it appeared that the Syrians were in fact being drawn into the conflict as the Army command announced today that Israeli jets shot down seven Syrian Mig fighters and that Israeli and Syrian troops had clashed directly in tank battles near Jazzin.

"We do not want to clash with even one Syrian soldier," the prime minister said. "I know President Hafez Assad can keep an agreement. He signed agreements with us and kept them meticulously. He also did not allow the terrorists to operate from the Golan Heights and Syrian territory afterward, and I expect him to do the same from Lebanese territory under his control."

Begin was referring to the 1974 separation of forces agreement in the Golan Heights that ended fighting between Israel and Syria there.

In his speech, Begin said that as soon as the Israeli Army establishes a secure 25-mile zone north of the Israeli frontier "our work will have been done and all fighting will cease." He added, "We do not want even one square millimeter of land, and we call for the restoration of the quiet border between Israel and Lebanon. We have reason to believe that this will be achieved."

Despite the reports of increased fighting today, there has been a sense of relief in Israel that the casualty figures released early this morning by the Army have been relatively light, given the size of the incursion and the level of Palestinian resistance. The Army command announced that 25 members of the Israeli defense forces have been killed and 96 wounded, mostly lightly. Seven are missing in action and one was captured, the Army announced.

The release of the casualty figures before the end of hostilities was unusual. During the 1967 and 1973 Middle East wars, the military withheld numbers of casualties in an effort to dampen public anxiety. In the 1973 war, families of servicemen killed were prohibited from placing death notices in newspapers.

An aide to the prime minister said that the absence of any casualty figures after two days of intensive fighting had prompted rumors that losses might be heavy and that the government decided for the sake of public morale to release the figures.

The Army announced that four Syrian Mig fighters were downed by Israeli jets in aerial battles in the vicinity of Beirut and south of the capital and that three more Migs were downed in a dogfight over the Galilee panhandle near the border. The Army said one of the Syrian pilots whose plane was hit over the Galilee parachuted into Israeli territory and was captured, and two other pilots also were captured, presumably in Lebanese territory controlled by the invasion force.

Military officials acknowledged for the first time publicly that there had been direct clashes between Israeli troops and the Syrian Army, citing tank battles in the vicinity of Jazzin. The Army spokesman said Syrian tanks were damaged, but that the numbers were unknown.

"The axis between Jazzin and Sidon is in the hands of our forces. We have emerged with the upper hand in all clashes with the Syrians. All of these encounters involved small units of tanks against small units of tanks, and small-scale air battles," the communique said.

In a communique issued tonight, the Army command said that at the end of 55 hours of fighting, all of the Israeli forces had reached their objectives "more quickly than called for in the battle plan and timetable."

An Army command spokesman said the forces were involved in "the cleaning up and securing of the area," and that the mop-up operation in Sidon was still under way today, although it could take longer because of the size of the city and continued resistance by Palestinian guerrillas.

Amid a clear consensus that Israel should continue the advance against Palestinian guerrillas, even if they seek refuge in Syrian-held territory, the Knesset (parliament) voted 94-3 against a no-confidence motion charging the government with "aggression." The motion was submitted by the communist Democratic Front for Peace and Equality.

Only eight members of the 50 members of the opposition party abstained. They were joined by one member of the Shinui Party in the most lopsided defeat of a no-confidence motion since Begin's Likud government was first elected in 1977.

In the past month, Begin's government barely has squeaked by on votes of no confidence on issues ranging from policies in the occupied West Bank to the state of the economy, and the vote tonight appeared to reflect the widespread public support in Israel for the government's declared intention of pushing Palestinian guerrillas out of artillery range of civilian settlements in the northern Galilee, while at the same time destroying the PLO military infrastructure in southern Lebanon.

In a military ceremony, Israel handed over the captured PLO stronghold at Beaufort Castle to Maj. Saad Haddad, leader of the Israeli-supported Lebanese Christian militias in southern Lebanon.

Although Beaufort is in the zone that is supposed to be controlled by the U.N. peace-keeping force, Haddad said his militias would remain in charge of the area.

Avi Pazner, spokesman for the Israeli Foreign Ministry, said Israel still regards the U.N. peace-keeping mandate in Lebanon as valid. "If we decide it is in our best interest to extend the mandate, it will be extended. First we have to clean up the areas where we have gone, and only afterward will we consider the long-range situation," Pazner said.

Meanwhile, U.S. special envoy Philip C. Habib met again tonight with Begin and his senior advisers, but he refused to discuss with reporters the nature of the talks.