TEL AVIV, Israel -- There is a new bumper sticker on the streets here these days, and it carries a blunt message: "Let's Get Out of Lebanon." Behind the stickers is an organization called Four Mothers, a group of women with sons in the Israeli army who are demanding an immediate pullout from the Israeli occupation zone in southern Lebanon. The nine-mile-wide swath of territory has been patrolled by the Israeli army and an allied Lebanese militia since 1985 as a buffer against attacks on northern Israel. But battles in the zone with Hezbollah guerrillas have taken an increasing death toll on the army in recent months, sometimes setting off rocket attacks on northern Israeli communities. Another Israeli soldier was killed in southern Lebanon Thursday when a rocket hit his tank. As the military casualties have increased, so has support for the mothers' group, which now says it has hundreds of active members and close to 15,000 signatures on its petitions. Another movement advocating a pullout was begun this month by Yossi Beilin, a member of parliament from the opposition Labor Party, and it says it has drawn drawn hundreds of backers. The emergence of the protest movements reflects wider stirrings of discontent among Israelis, who are still under the pall of the deaths this month of 12 naval commandos in a failed raid in Lebanon, and five Israeli civilians in a triple suicide bombing in Jerusalem. A total of 34 soldiers have been killed in Lebanon this year, and 20 Israelis have died in two suicide bomb attacks in recent weeks in Jerusalem. The losses have left many Israelis grieving and confused about what path the government should take to stop the bloodshed. "There are definite signs of fatigue in Israeli society," Lt. Gen. Amnon Shahak, the army chief of staff, said in remarks broadcast this week on army radio. "Some of us want a quick and clear answer, and I don't believe that we have a single, sharp and agreed response that can be implemented quickly without risks and without being ready to pay a price." Anguished parents of soldiers and of victims of the violence have added their voices to the debate. The father of a commando killed in Lebanon issued a plea to Prime Minister Benjamin Netanyahu over the radio to cut the Gordian knot. "If it's going to be war, then make war, and if it's going to be peace, make peace," he said. The mother of a girl killed in the last Jerusalem bombing blamed the government for its treatment of Palestinians, which she said bred suicide bombers. "When you put people under border closure, when you humiliate, starve and suppress them, when you raze their villages and demolish houses, when they grow up in garbage and in holding pens, that's what happens," the bereaved mother, Nurit Peled-Elchanan, said in an interview with the newspaper Haaretz. When Netanyahu, a childhood friend, called to console her, she asked him, "What have you done?" The father of a commando who survived the fighting in Lebanon appealed to Netanyahu in a television interview. "This is a child of peace," he said of his son. "If he were told, 'Go now and shake the hand of the Hezbollah chief in the name of Israeli peace,' he would do it. He doesn't want wars, and neither do we." The calls to leave Lebanon have cut across party lines. Some Cabinet ministers, including the usually hawkish Ariel Sharon, have suggested an early pullback, while several leaders of the opposition have rejected the idea. Four Mothers, an independent group that includes supporters of various parties, was formed by four women living in northern Israel after 73 soldiers were killed in February in a collision of two helicopters ferrying troops to Lebanon. "We couldn't sleep that night until we heard the voices of our children telling us that they were OK," said Miri Sela, one of the mothers, who lives in Kibbutz Mahanayim, less than 10 miles from the Lebanese border. "That evening transformed us from people resigned to the idea that there is no other choice, to those determined to find a solution." "When our sons came home for the funeral of a friend killed in the crash, we heard them saying, 'Now it's our turn to make the sacrifice for this country,"' Mrs. Sela recalled. "I shouted: 'No! It won't happen! This god will not get any more sacrificial blood. Enough!"' The mothers have held demonstrations near the Defense Ministry in Tel Aviv and lobbied Cabinet ministers and members of parliament. They contend that the army's continued presence in Lebanon has failed to shield northern Israel from rocket attacks, while bogging down the military in a costly guerrilla war that it cannot win. The women assert that withdrawing Israeli troops to the border would remove the cause for anti-Israeli violence in Lebanon while leaving Israel the option for a powerful, internationally accepted military response to any possible attack across the frontier. Representatives of the group met last Friday with Defense Minister Yitzhak Mordechai to argue their position. He reportedly told them that a unilateral withdrawal from Lebanon would only invite attacks across the border by guerrillas of Hezbollah, or the Party of God, which is backed by Iran and Syria. But Meira Har-Zahav, one of the women who attended the meeting, rejected Mordechai's logic. "Hezbollah's aim is not to attack the northern settlements, but to evict us from Lebanon," she said. "The risk to the lives our sons is greater than any possible gain from their staying there. Has anyone defeated a guerrilla army? Hundreds have died in this swamp, and it hasn't brought us anything. We have to take the risk and leave." .