However, Israel wants Hezbollah first to pull back from the Israel-Lebanon border and release two soldiers it captured last week, while Hezbollah wants the cease-fire first and then talk with international mediators about an exchange of prisoners.
A senior Israeli official said Prime Minister Ehud Olmert had conveyed Israel's position to Italy's prime minister, who is trying to broker a cease-fire deal.
Israel had previously demanded the full dismantling of Hezbollah as a condition for ending hostilities. However, the senior official said Israel would agree to Hezbollah merely leaving the border area with the Lebanese army taking its place.
Meanwhile, Hezbollah-backer Iran said Monday that a cease-fire and a prisoner exchange would be possible.
"We believe that we should think of an acceptable and fair (deal) to resolve this," Foreign Minister Manouchehr Mottaki said after talks with Syrian Vice-President Farouk al-Sharaa in Damascus. "In fact, there can be a cease-fire followed by a prisoner swap."
Iran and Syria are the principal sponsors of Hezbollah, and the two countries have applauded Hezbollah's capture of two Israeli soldiers, which triggered the Israeli offensive in Lebanon that has killed nearly 200 Lebanese, most civilians, and wounded more than 400 others.
An open microphone Monday caught President Bushto complain about Syria and Hezbollah, reports CBS News White House correspondent Peter Maer.
In other developments:
A senior U.N. envoy said Monday he will present Israel with "concrete ideas" to end the fighting after meeting with Lebanon's prime minister. But Vijay Nambiar, U.N. Secretary-General Kofi Annan's special political adviser, warned that "much diplomatic work needs to be done."
He said he will go to Israel shortly and was optimistic about his peace efforts. "We have made some promising first efforts on the way forward," he said.
"We believe that we should think of an acceptable and fair (deal) to resolve this," Iranian Foreign Minister Manouchehr Mottaki said after meeting with Syrian Vice President Farouk al-Sharaa in Damascus. "In fact, there can be a cease-fire followed by a prisoner swap."
"The circumstances prevailing in the region are not in the interests of the Zionist entity," he said, referring to Israel. "The attack launched by Israel was orchestrated."
Although Israelis tell CBS News chief foreign correspondent Lara Logan the attacks on Haifa are like attacks on San Francisco would be to Americans, Mayor Yona Yahav tells Logan it's not unexpected. "We are patient, we are strong, and we can take it."
The strikes in Lebanon have been concentrated in a very small area about one square mile, reports CBS News correspondent Elizabeth Palmer in Beirut. Outside the capital, specific targets include crucial transportation links like bridges and roads, choking off normal movement.
Lebanese security officials said as the death toll from the conflict rose to more than 200 — 196 in Lebanon, according to the officials, and 24 in Israel.
Meanwhile, the very first American citizens were air-lifted to safety Sunday night. The 21 Americans, all college students, went to Cyprus on a Marine helicopter and another small group was expected to travel that way Monday.
It will be Tuesday at the earliest before large scale evacuations can begin, reports CBS News national security correspondent David Martin. Then, a Greek commercial vessel, the Orient Queen, with capacity to carry 750 passengers, will be under U.S. charter and available to ferry evacuees from Lebanon to Cyprus.
A Greek cruise ship chartered by French government was due to arrive Lebanon Monday to evacuate 900 French and 300 other European nationals to Cyprus, reports CBS News correspondent Elaine Cobbe in Paris. French ambassador Hadelin de la Tour du Pin said he had received assurances from Israeli government that the ship would receive safe passage to Lebanon and then to Cyprus.
The evacuated students say there is anger and resentment among the Americans they left behind in Beirut, reports CBS News' Amy Guttman. They cite European nationals whose governments acted swiftly to evacuate them. Guttman says there are reports that some Americans have been told by the U.S. Embassy that they could be stuck in Beirut for as much two more weeks.
Israeli officials accused Syria and Iran of providing Lebanese guerrillas with sophisticated weapons, saying the missiles that hit Haifa had greater range and heavier warheads than those Hezbollah had fired before.
The United States, Israel and Lebanon are not in a good position, Michael O'Hanlon of the Brookings Institution said on CBS News' The Early Show.
"Israel doesn't have the military power to stop this. It's the terrorist and insurgent movement, and it's very hard to stop this sort of thing with artillery and airplanes," O'Hanlon said. "We don't have enough influence over any of the parties, and the Lebanese government can't really reign in Hezbollah because it's not strong enough."
"The world is not sure how to get out of this and is getting ready for the worst. That's why we're talking about evacuation plans of tens of thousands of people," O'Hanlon told Early Show co-anchor Harry Smith.