srael declared tonight that it would extend the cease-fire in Lebanon to include Palestinian guerrilla forces, but warned that Israeli troops would renew their attacks if fired on by the Palestinians.

Israeli officials did not explain the extension of the cease-fire that Israel declared with Syria yesterday. The new cease-fire went into effect at 9 p.m. (3 p.m. EDT), an hour after the surprise announcement by the office of Prime Minister Menachem Begin, and appeared to be holding four hours later.

Although Israeli Foreign Minister Yitzhak Shamir had a day of meetings with U.S. special envoy Philip C. Habib--who had been known to be pressing for a cease-fire with the Palestinians as a prelude to Israeli withdrawal from Lebanon--Israeli sources insisted tonight that pressure from the United States was not a factor.

"Why is it every time we make a decision to try to calm the situation, it has to be the result of pressure from the Americans?" one Israeli official asked.

U.S. officials would not discuss the nature of negotiations with Israeli officials.

Shamir told Israeli radio Saturday night that Israel wants the help of the United States to win a diplomatic agreement that will preserve its military gains against the Palestinian guerrillas in Lebanon, United Press International reported from Tel Aviv.

"We are continuing with our contacts to cooperate with our friends the Americans to achieve an agreement that will bring peace and stability to the Middle East," he said.

Israel took the unilateral step as a national debate emerged over whether to advance the invasion farther into Lebanon or broaden the cease-fire as a prelude to withdrawing Israeli forces to their own frontier.

Uri Porat, Begin's press secretary, said that following Israel's cease-fire on all fronts with the Syrian forces in Lebanon, Palestinian gunners in Beirut had continued to shell Israeli forces.

"Nevertheless, we have decided to make a new attempt in the cease-fire . . . . If the terrorists, in spite of this, continue their attacks, we will feel free to react with all our might," Porat said.

On Friday, Defense Minister Ariel Sharon made it clear that the Syrian-front cease-fire did not apply to Palestinian guerrillas and that the Israeli Army would continue to flush them out.

Shamir emphasized that the decision was unilateral and not the result of "contacts with outside elements."

Referring to the cease-fire with the Syrians, Shamir said in a television interview, "We announced the cease-fire yesterday of our own volition. It is a unilateral cease-fire. The Syrians maintained it generally. The terrorists did not honor the cease-fire.

"Today, we decided to make an attempt, but not as a result of contacts with outside elements. This was at our initiative. We decided to make a further attempt this evening to cease fire, and if the terrorists also cease firing, firing will stop."

Israeli sources said the cease-fire applies to all fronts where Israeli troops are in confrontation with Palestinian forces, although its primary focus is the area just south of Beirut. Israeli troops are dug in north of Damour, where they have traded artillery fire for two days with PLO concentrations in Khalde, near the Beirut International Airport.

Israeli officials stressed that the Army would continue to track down Palestinian guerrillas south of the foward line.

But the last word on the issue is far from being heard from those in the military establishment and in the Knesset (parliament) who feel that Israel is passing up a unique opportunity and cutting short its objectives.

Meanwhile, mainstream opposition Labor Party leaders have suggested tentatively that the government should not set too ambitious military and political objectives in Lebanon.

Labor Party leader Shimon Peres and Labor Knesset member Abba Eban, while stressing their support of the invasion and its original objectives, said that the government should resist temptation to try to establish a new political order in Lebanon and be satisfied that the Army has crippled the Palestine Liberation Organization military infrastructure.

Before the newly announced cease-fire, the small, leftist Shinui Party of the Knesset and one member of the Labor Party, Josi Sarid, called outright for such a move and were joined by the Peace Now movement and other peace groups in Israel.

Because of a strong national consensus favoring the invasion, the peace activists said, their cause has hardly been noticed by most of the public and, in fact, has generated some antagonism against members.

"But we have seen signs of divisions on this issue. We've talked with a lot of people who think the Army has gone far enough and should withdraw immediately. They say, 'What more is there to accomplish? We have the 40 kilometers, isn't that enough?' " said Judy Blanc, a Peace Now activist.

She was referring to the 25-mile "artillery free" zone that the government set as its initial objective to free northern Israeli settlements from the threat of PLO artillery based in South Lebanon.

Proponents of a more aggressive stance, including some senior Army officers and, to a degree, the Army chief of staff, Maj. Gen. Rafael Eitan, long have argued that the source of Lebanon's ills has been the dominance of that war-shattered country by the PLO and the 25,000 Syrian troops that came ostensibly as an Arab League peace-keeping force to stop the 1975-1976 civil war, even though Israel tacitly accepted the move at that time.

However, even if the Israeli Army did succeed in pushing the Syrian forces out of Lebanon, the Israeli government, in its quest for a political solution to the Lebanese-PLO problem, would have nobody with whom to make a deal for diluting the PLO influence there. Begin's government has made it clear it will never talk with the PLO.

Without the Syrians, the central Lebanese government would be powerless to exercise day-to-day authority, much less effect a negotiated political settlement. If the Israelis went to the Christian Phalange forces led by Bachir Gemayel, they would be undercutting the very government that they profess to want for a free and independent Lebanon.

For Israel's purposes, the ideal solution would be for the PLO to quit Lebanon and go to Syria, where presumably they could be contained by the strong hand of President Hafez Assad, the official said, noting that the Syrians have prevented terrorist infiltration into the Golan Heights since 1974.

Any Palestinian guerrillas who remain, the official said, would be assimilated into the "new political order" in Lebanon.

"We had the same situation in the West Bank," he added. "They take off their uniforms, get rid of their guns and accept the reality."