MIAMI, AP – President Bush insisted anew Monday that any Mideast cease-fire be accompanied by a wider agreement. “We want there to be a long-lasting peace, one that is sustainable,” he said as Israel cut short a halt in bombing and launched new strikes in southern Lebanon.

Bush said he 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.

“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, speaking after a meeting with Cuban-American business leaders in a Miami restaurant.

“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.”

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.

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 Taibe were meant to protect ground forces operating in the area and were not targeting anyone or anything specific, the army said.

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.

State Department spokesman Adam Ereli had noted in a statement late Sunday that, in connection with the halt in bombing, “Israel, of course, has reserved the right to take action against targets preparing attack against it.”

Bush on Sunday had renewed his call for a “sustainable peace” and cautioned Israel to spare civilians in its military attacks on the Hezbollah militia.

But he stopped short of calling for an immediate cease-fire, opting instead for a United Nations resolution calling for Hezbollah to lay down its arms and an international force to help the Lebanese Army keep the peace.

Bush monitored the crisis 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.

Before leaving Jerusalem on Monday, Rice told reporters she would seek a cease-fire agreement as well as a long-term settlement in the conflict this week through a U.N. Security Council resolution.

“I am convinced that only by achieving both will the Lebanese people be able to control their country and their future, and the people of Israel finally be able to live free of attack from terrorist groups in Lebanon,” she said.

But after Rice departed, hopes the two-day halt in bombing would become a longer term cease-fire dimmed when Israel’s defense minister, Amir Peretz, told parliament that Israel would “expand and strengthen” its attack on Hezbollah.

“It’s forbidden to agree to an immediate cease-fire,” Peretz said.

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.

While he mourned the deaths, Bush continued to press for what he believes will be a longer-lasting cessation of violence.

The U.N. Security Council met a day after a draft resolution was circulated calling for an immediate halt to the fighting and seeking a wide new buffer zone in south Lebanon monitored by an international force and the Lebanese army.

As diplomacy dragged on, impatience rose.

Lebanese Prime Minister Fuad Saniora said the talk of a larger peace package must wait until the firing stops. British Prime Minister Tony Blair, who spoke on the phone with Bush on Sunday, said Washington must work faster to put together the broader deal it seeks. “We have to speed this whole process up,” Blair said. “This has got to stop and stop on both sides.”

Rice, who met with Israeli leaders on Sunday, scuttled her 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!”