JERUSALEM — Israel brushed aside mounting calls yesterday for a cease-fire in Lebanon. Its army made clear that it planned to keep up its assault for at least a week and had not ruled out a ground invasion.

Buoyed by support from Washington for rooting out Hezbollah rockets from southern Lebanon, the army treated parts of the border area as a free-fire zone. It hit at least two cars with rockets as they sought the relative safety of the city of Tyre.

Secretary of State Rice was setting out for the Middle East last night, but aides said calling a cease-fire was not on her agenda unless it involved the disarming of the Iranian-backed Hezbollah.

“The purpose is to maintain a sustainable cease-fire,” President Bush’s chief of staff, Josh Bolten, said. “It is sustainable only if we get to the root problem, which is Hezbollah, a terrorist organization.” That uncompromising response will disappoint those at the United Nations and in Europe who believe that a cease-fire should be the primary aim.

Prime Minister Olmert said he accepted proposals for an international force for southern Lebanon. But the broad powers he envisaged for it appeared to rule out any prospect of it ever taking shape.

“Israel is ready to see deployment of a force with military capabilities and combat experience made up of troops from European Union countries,” he told the German foreign minister, Frank-Walter Steinmeier.

But in addition to monitoring Lebanon’s border with Israel, the force would have to control crossings between Syria and Lebanon. That would require some 20,000 troops, and Lebanon would see such a mandate as tantamount to an occupation.

In Beirut, the United Nations’ emergency relief coordinator, Jan Egeland, toured parts of the southern suburbs, which have been devastated by airstrikes, and accused the Israelis of violating international humanitarian law.

“It is horrific,” he said as he visited the Haret Hreik district.”I did not know it was block after block of houses.”

Despite 11 days of bombardment, Hezbollah launched salvos of rockets into northern Israel, killing two people in Haifa and wounding more than 30.

Israel’s chief of staff, Lieutenant General Dan Halutz, said his forces needed weeks to do their work.”I don’t want to set a date,” he said, “but we’re trying to shorten the operation and still achieve our goals.”

As senior diplomats from Britain, Germany, and France arrived in Israel to try to coax it toward a cease-fire or at least restraint, General Halutz said: “The foreign ministers do not determine our time limit. The Israeli government does that.”

In London, ministers insisted that there was no rift between the Foreign Office and no. 10 after a Foreign Office minister, Kim Howells, speaking in Beirut, accused Israel of using disproportionate force and destroying Lebanon. He returned to the theme yesterday after visiting Haifa.

“I am very disturbed the more I hear about the extent of this campaign,” he said. “At some stages there are 60 jets out there over the Mediterranean waiting to hit targets.”

The Israeli foreign minister, Tzipi Livni, said she hoped that Mr. Howells, having visited northern Israel, where some 2,000 missiles have struck, understood that the country “had a duty to defend its citizens.”

America supports Israel’s declared aim of forcing the implementation of U.N.resolution 1559, which calls for the disarming of Hezbollah and the deployment of the Lebanese army to southern Lebanon. It swept aside a Syrian offer of direct talks on the crisis.

The American ambassador to the United Nations, John Bolton, said, “Syria does not need dialogue to know what to do; they need to lean on Hezbollah.”

The Americans are hoping to use moderate Arab states such as Saudi Arabia and Egypt to convince Syria that it should cut its ties with Iran. Such a move would greatly weaken Hezbollah.