MIAMI (AP) – President Bush insisted anew Monday that any Mideast cease-fire be conditioned on a wider agreement and said he would look to the United Nations to act to establish “a long-lasting peace, one that is sustainable.”

As Israel cut short a halt in bombing and launched new strikes in southern Lebanon, Bush spelled out a series of what he called “clear objectives” to accompany a halt in the fighting.

“Iran must end its financial support and supply of weapons to terrorist groups like Hezbollah. Syria must end its support for terror and respect the sovereignty of Lebanon,” Bush said in a speech at the Port of Miami.

Bush planned to meet later Monday in Washington with Secretary of State Condoleezza Rice, who cut short her diplomatic mission and was returning from the Middle East.

“As we work with friends and allies, it’s important to remember this crisis began with Hezbollah’s unprovoked attacks against Israel. Israel is exercising its right to defend itself,” Bush said, resisting mounting international pressure for an immediate cease-fire.

“We mourn the loss of innocent life, both in Lebanon and Israel,” he added.

Other conditions for a cease-fire include a requirement that a multinational force be quickly sent to southern Lebanon, Lebanon’s government must be “empowered to exercise sole authority over its territory” and two Israeli soldiers taken by Hezbollah be returned.

Israeli warplanes carried out airstrikes in southern Lebanon on Monday, hours after agreeing to a 48-hour halt in the airstrikes while investigating a bombing that killed nearly 60 Lebanese civilians, mostly women and children seeking shelter.

Earlier, Bush said after meeting with Cuban-American business leaders at a Miami restaurant, “We want there to be a long-lasting peace, one that is sustainable.”

“I’ll speak to Condi Rice when she gets back tonight, talk about what she saw, what she heard in the Middle East. And, of course, there’ll be a way forward in the Security Council later this week,” Bush said.

“I assured the people here that we will work toward a plan at the United Nations Security Council that addresses the root causes of the problem, so that whatever comes out of the Security Council will be able to last and that the people of Lebanon and Israel will be able to remain in peace,” Bush said. “That’s what we want.”

Israel had left open the option it might hit targets to stop imminent attacks or if the military completed its inquiry within 48 hours. Monday’s airstrikes near the village of Taibeh were meant to protect ground forces operating in the area and were not targeting anyone or anything specific, the army said.

The Israelis told U.S. officials that ground operations were continuing, and Monday’s renewed air strikes were close-in support for operations against rocket launchers that were about to be used, said a U.S. official, speaking on condition of anonymity.

There was an expectation that Israel would respond to threats of attack being prepared against it, the official said, saying there was no authorization to speak publicly on this subject.

The official added that it’s important that the aerial suspension be implemented to allow humanitarian aid to be delivered and safe passage to continue and that the United States believes suspension of air activity serves the purpose of investigating and preventing incidents like the one in the south Lebanese village of Qana, where dozens of civilians were killed by an Israeli attack.

The administration already had been immersed in tough diplomacy before Sunday, with Rice flying around the world and U.S. officials conferring steadily with counterparts at the United Nations, when international outrage flared.

Bush monitored the crisis over the weekend through phone calls with his top advisers as images of children’s bodies in the building’s ruins flashed on television screens across the world. Bush spoke three times with Rice, who cut short her diplomatic mission in the Mideast and headed back to Washington.

The U.N. Security Council met in emergency session and passed a statement expressing “extreme shock and distress” over Israel’s bombing of civilians. U.N. Secretary-General Kofi Annan sharply criticized world leaders _ implicitly Washington _ for ignoring his previous calls for an immediate cease-fire.

Rice, who met with Israeli leaders on Sunday, scuttled a trip to Lebanon after the bombing, which inflamed sentiment against the United States and Israel. Some 5,000 protesters gathered in downtown Beirut, attacking a U.N. building, burning American flags and shouting: “Destroy Tel Aviv! Destroy Tel Aviv!”