Israel's government is losing domestic support for its conduct of the conflict against Hizbullah guerrillas in Lebanon, and doubt is growing among Israelis that they are winning the war, according to polls published Friday. The army's failure to end incessant attacks is likely one reason for the drop in the government's popularity figures. A poll in the Yediot Aharonot newspaper showed 37 percent of the 500 people questioned believed Israel would cripple Hizbullah, compared with 40% in a previous survey. 17% thought Israel would lose the war and Hizbullah would return to south Lebanon, up from 13% previously, said the poll conducted by the Dahaf organization. It had a margin of error of 4.5%. The percentage of people supporting a broad ground operation to push Hizbullah guerrillas beyond the range of short-range rockets fell to 64% from 73%, the poll said, indicating a growing - though still a minority - public desire for diplomatic initiatives. On Wednesday, the Security Cabinet gave Prime Minister Ehud Olmert the authority to send more troops into south Lebanon. Officials said Israel will hold off on any new offensive for a few days for diplomatic efforts to play out at the UN Security Council, where the United States and France were working on a cease-fire resolution that could come to a vote as early as Friday. The Dahaf survey showed Olmert's personal approval rating fell to 66% from 73%. Another poll of 570 Israelis, conducted by Dialogue for the Haaretz daily, said just one Israeli in five believes that if the war ended now, it could be considered a victory, while 30% said Israel is losing the war and 44% said neither side would emerge a winner. The poll's margin of error was 4.8%. Though the Security Cabinet vote overwhelmingly approved broadening ground operations - nine in favor with three abstentions - reports indicate that divisions run deeper in Olmert's inner circle. Haaretz reported Olmert vetoed an appearance at the Security Council by Foreign Minister Tzipi Livni, who has been counseling military restraint and greater attention to diplomacy. On Thursday, three of Israel's most successful left-wing authors and intellectuals - Amos Oz, David Grossman and A.B. Yehoshua - joined together to urge Olmert to respond positively to an initiative by Lebanese Prime Minister Fuad Saniora offering to deploy the Lebanese army to southern Lebanon, aided by an international force, and an exchange of prisoners. "Israel was right when it chose to respond with force to Hizbullah's violent provocation," said Oz, an eloquent voice of the Israeli left. But the Lebanese plan "was not only a turning point, it was a victory for Israel's basic demand," Oz said. Israel should have told Saniora his plan was a good basis for negotiation and halted its offensive.