TIBERIAS, Israel — Israel said yesterday that its armed campaign in Lebanon would continue “for weeks” despite doubts over its ability to crush Hezbollah and the arrival of United Nations negotiators in Jerusalem.

The U.N. team said it had presented both sides with “concrete ideas” to end the conflict while Israel’s foreign minister, Tzipi Livni, said her country was “beginning a diplomatic process alongside the military operation.”

But Israel’s deputy army chief, Moshe Kaplinsky, said the bombing in Lebanon would continue for at least a fortnight as the Israeli air force picked off targets to achieve “very clear goals.”

One of those goals is the assassination of the Hezbollah leader, Sheik Hassan Nasrallah, whom the Israeli military recognizes as a charismatic and intelligent foe.

On a wider scale however, planners say there is a limited amount Israel can do to put Hezbollah permanently out of action.

It can sometimes succeed in hitting the supply of weapons from Syria, Hezbollah’s sponsor, and yesterday said Israeli aircraft had destroyed several trucks carrying weapons since current hostilities began a week ago.

But an air campaign cannot hope to destroy the supply lines nor all of Hezbollah’s well-hidden, well-distributed weapon stockpiles.

Growing civilian casualties in the country also appear to have the effect of rallying, not weakening, support for the group.

“What Israel wants is better security when the dust settles,” said Shlomo Brom, an ex-strategy chief for the Israeli army and military adviser to prime ministers Yitzhak Rabin, Shimon Peres, and Binyamin Netanyahu.

He added, “If Israel could have its wish, it would wish for the total disarmament of Hezbollah as called for in U.N. resolution 1559, but I am pessimistic about the capacity of the Lebanese government and the will of the international community to do this.

“What is feasible is a buffer zone in southern Lebanon, where the only presence allowed is the Lebanese army and an effective international force, like the NATO force in the Balkans.”

The campaign in Lebanon has overwhelming popular support in Israel, where 90% of people back it, according to a poll released yesterday. The same poll also showed Prime Minister Olmert, scoring a 78% approval rating as he continued to present a public attitude of “no compromise, no surrender.”

In his first address to the nation since the crisis began, Mr. Olmert called for the unconditional release of two Israeli soldiers being held by Hezbollah.

“Israel will not be held hostage — not by terror gangs or by a terrorist authority or by any sovereign state,” he said.

However, just hours after Mr. Olmert’s speech, the public security minister, Avi Dichter, said Israel would eventually have to contemplate a prisoner exchange.