UNITED NATIONS — As international demands for a cease-fire intensified yesterday and Britain and the United Nations called for an international force to be sent to southern Lebanon, Prime Minister Olmert said military operations will not end until Hezbollah is removed from Israel’s northern border.

Israel did not officially respond to Prime Minister Blair and Secretary-General Annan’s proposal for an international force. But Mr. Olmert’s statement seemed to stress the existing conditions set by the Security Council, which authorize the deployment of government-controlled troops in southern Lebanon once Hezbollah and other militias are disarmed.

“Once we are finished with Hezbollah, as far as I am concerned, any force that wants to could be deployed there,” a senior Israeli official told The New York Sun, speaking on condition of anonymity because Jerusalem had not yet set a policy on the issue.

In a barrage of statements, world leaders were split along two camps. One side, centered around the United Nations, pushed for an immediate cease-fire, while the other, led by America, backed Israel’s efforts to neutralize Hezbollah.

“The majority of the international community supports our battle against the terror organizations and our efforts to remove this threat of the Middle East,” Mr. Olmert told the Knesset in his first formal speech since the start of the hostilities. “We will continue to operate in full force until we achieve this.”

Israel will “insist on compliance with the terms stipulated long ago by the international community,” he said: the release of Israeli hostages, the deployment of the Lebanese army in southern Lebanon, and the “expulsion of Hezbollah from the area.”

The barrage of missiles from Lebanon into Israel intensified last night, as did the Israeli operation to dismantle Hezbollah’s military infrastructure, which Iran and Syria have built up and supplied since the early 1980s.

When they set up Hezbollah after Israel’s 1982 invasion of Lebanon, a Farsi broadcaster, Menashe Amir, said, the Tehran mullahs sent “around 400 elite military Revolutionary Guard advisers” to southern Lebanon.That number has been maintained since then, he added. Mr. Amir estimated that Iran has poured more than $500 million in aid into Hezbollah since 1982.

Military sources quoted in Israeli press reports said yesterday that they intercepted an Iranian-made Zilzal missile capable of traveling more than 100 miles, far enough to hit major Israeli population centers around Tel Aviv. The army announced a major call-up of reserve troops to be deployed in the West Bank while regular forces stationed there move the Lebanese front.

Dispatched by President Chirac to Beirut yesterday, Prime Minister de Villepin of France asked for an “immediate humanitarian truce.” But at the United Nations, the French ambassador, Jean-Marc de la Sabliere, said, “The question of disarming the militias and extending the authority of the Lebanese government to the whole territory is key.”

Diplomats debated whether a ceasefire or disarmament should come first.

“You would have a cease-fire in a matter of nanoseconds if Hezbollah and Hamas would release their kidnap victims and stop engaging in rocket attacks and other acts of terrorism against Israel,” the American ambassador to the United Nations, John Bolton, said.

“The main thing now — the council should take a position on how we can implement a cease-fire,” Qatar’s ambassador, Nassir Adulaziz al-Nasser, who represents the Arab group at the Security Council, told the Sun. He said the Arabs would support the idea outlined by Messrs. Annan and Blair.

In St. Petersburg, Russia, yesterday, Mr. Blair called for the expansion of the existing 2,000-strong U.N. observer mission in southern Lebanon, known as UNIFIL, strengthening its mandate, and, according to sources familiar with the plan, adding 8,000 mostly European troops to it.

“The mission will have to be far more specific and clearer, and the force employed will have to be far greater,” Mr. Blair said.

But he acknowledged that any such deployment would “take time.” The Security Council, which Mr. Annan has said would have to approve the plan, is not expected even to start discussing the matter before the end of the week, when Mr. Annan’s representatives are expected to brief the council on their meetings, diplomats said yesterday.

According to press reports from Jerusalem, Israel’s Foreign Ministry supports the idea of an international force, while Mr. Olmert’s top advisers oppose it, as does the usually dovish defense minister, Amir Peretz.

A three-man U.N. team, dispatched by Mr. Annan to the region last week, arrived in Israel yesterday and planned to relay the idea to Foreign Minister Tzipi Livni after receiving a nod from Prime Minister Siniora of Lebanon. Mr. Olmert so far has been cool to the team, which is currently the only known diplomatic mission to mediate between Israel and Lebanon.

Since the hasty retreat of U.N. peacekeepers deployed on the Israel-Egypt border on the eve of the 1967 war, Israelis have eyed foreign troops with suspicion. While some, like the American-led, non-U.N. interim force in the Sinai Peninsula, have had some success, others, such as UNIFIL, have created more problems than they solved, the senior Israeli official said.

When they are stationed among Arabs, international forces often adopt the Arabs’ point of view, the official said. While providing no protection for Israelis, he said, the troops create problems for Israel’s army as it carries out defensive operations like the current campaign in Lebanon.