The Bush administration is pushing for quick approval of a cease-fire resolution from the UN Security Council, but is warning the action is unlikely to put an immediate stop to the fighting in the Israeli-Hizbullah conflict. US officials say they expect the council to vote by Tuesday on the resolution designed to stop the major military operations that have been disrupting life in Lebanon and Israel for more than three weeks. The fighting between Israel and Hizbullah guerrillas in Lebanon intensified over the weekend as diplomatic work was under way at the United Nations. Security Council experts went over the draft for several hours Sunday, and diplomats said there was a widespread feeling that it did not sufficiently take Lebanon's concerns into account. Several members suggested amendments. President George W. Bush, on a 10-day vacation at his ranch, left the negotiations to his diplomatic aides. Secretary of State Condoleezza Rice and National Security Adviser Stephen Hadley spent the weekend on the president's grounds and kept him updated. Bush stayed in seclusion and had not commented publicly about the draft, reached through negotiations between the US and France and announced at the United Nations early Saturday. But he planned to speak to reporters about the developments Monday morning, with Rice at his side. The draft calls for Hizbullah to stop all military operations and for Israel to stop its offensive military drive into Lebanon. The proposal would allow Israel to strike back if Hizbullah were to break a cease-fire. Lebanon urged the council to revise the resolution to demand that Israel pull its forces out of the country once hostilities end and hand over its positions to UN peacekeepers. The draft made no mention of an Israeli withdrawal. The United States wants a second resolution that would form an international force that would move into Lebanon and help take control of the southern part of the country, where the Hizbullah has been operating. "We're trying to deal with a problem that has been festering and brewing in Lebanon now for years and years and years," Rice said Sunday. "And so it's not going to be solved by one resolution in the Security Council. "I can't say that you should rule out that there could be skirmishes of some kind for some time to come," she said. The Lebanese parliamentary speaker, a prominent Shi'ite who has been negotiating on behalf of Hizbullah, rejected the US-French plan because it did not include an immediate cease-fire and withdrawal of Israeli troops. US officials seemed to acknowledge that they don't expect Hizbullah to comply with the resolution if it is approved. Rice said that once the resolution passes, "then we'll see who is for peace and who isn't." Hadley said Hizbullah's response to an approved resolution would be a "clarifying moment." "I don't think you'll see an instantaneous end to the violence," Hadley said. "As you know, historically, these cease-fires take some time to go into effect, particularly if, unfortunately, Hizbullah were to reject it."