HAIFA, Israel — For many Israelis, the latest deadly attack on Haifa was a reminder of the need to press a campaign against the Lebanese militia despite a flurry of diplomacy aimed at calming the conflict.

“It’s tough to see the damage in Lebanon, but we have no choice but to defend ourselves,” said Oren Naidek, a supervisor at a chemical plant in Haifa bay who sent his wife and three small children south soon after the outbreak of fighting on July 12.

A dozen Hezbollah rockets crashed into outlying districts of Haifa on Sunday, this latest Katyusha salvo killing two people and wounding 14 just minutes after a solidarity visit to the city by French Foreign Minister Philippe Douste-Blazy.

Israel launched widespread airstrikes on Lebanon following a Hezbollah border ambush in which eight Israeli soldiers were killed and two others abducted.

But at Sunday’s weekly Cabinet session there was little of Prime Minister Ehud Olmert’s earlier tough talk. Instead, a subdued-looking Olmert mourned the dozens of Israelis who have died in the flare-up, praised the armed forces for their fortitude and vowed government help for northern Israel’s ailing local economy.

“I deeply appreciate the displays of caring and mutual responsibility” by Israelis for one another, Olmert said.

Western powers agree that, at the end of Israel’s operations, Hezbollah should not return to its previous position of straddling the southern Lebanese border. But few, if any, foreign governments would want to see this achieved as a result of a new invasion of southern Lebanon by Israel, which pulled its forces out of the area six years ago.

Olmert, who also has his hands full dealing with continued Palestinian rocket fire from the Gaza Strip, would seem to agree.

“No one want to get mired in the Lebanese swamp again,” said Immigration Minister Ze’ev Boim, an Olmert confidant.

Israeli commanders say the militia is down to half strength. But the Jewish state has failed to hit Hezbollah chief Sheik Hassan Nasrallah and put an end to his taunting televised statements.

For Israel’s top ally, the United States, the road forward appears clear — at least, in the short term.

Washington wants Hezbollah bested, both to improve Israel’s national security and to send a deterrent message to its patrons, Iran and Syria.

“Resolving the crisis demands confronting the terrorist group that launched the attacks and the nations that support it,” President Bush said Saturday in his weekly radio address.

“Their actions threaten the entire Middle East and stand in the way of resolving the current crisis and bringing lasting peace to this troubled region.”

The U.S. secretary of state, Condoleezza Rice, is scheduled to arrive in Israel on Monday for talks in which, according to Jerusalem sources, she will make clear that the United States will not block the Lebanon offensive for now.

As if to underscore the support, The New York Times reported that the Bush administration had approved an emergency shipment of advanced weaponry to Israel, including possibly “bunker-buster” bombs that the air force could use to crack the fortified command posts used by Nasrallah and his top comrades.

But weighed against Washington’s backing are the misgivings of the European Union, whose goodwill Olmert had been cultivating in hope of pushing through his now moribund plan for selective Israeli withdrawals from the West Bank.

Douste-Blazy, who had criticized Israel’s shelling of Lebanon as “disproportionate,” sounded more conciliatory during his Haifa visit but still spoke in terms of a truce rather that Hezbollah’s ouster.

“My message is the same — it is one of solidarity with the victims,” he told reporters.

“My question to Jerusalem and Beirut is the same — how do we reach as quickly as possible a cease-fire, responding to Israel’s legitimate right to live safely, and a cease-fire that will preserve this Lebanese state whose survival is in the interest of Israel?”