An Israeli airstrike on Beirut killed a senior Hezbollah commander on Tuesday as cross-border rocket attacks by both sides increased fears of a full-fledged war in the Middle East and Lebanon said only Washington could help end the fighting.

Hezbollah early on Wednesday confirmed senior commander Ibrahim Qubaisi was killed by Israeli airstrikes on Tuesday on the Lebanese capital as Israel announced earlier. Israel said Qubaisi headed the group's missile and rocket force.

Israel's offensive since Monday morning has killed 569 people, including 50 children, and wounded 1,835 in Lebanon, Health Minister Firass Abiad told Al Jazeera Mubasher TV.

The new offensive against Hezbollah has stoked fears that nearly a year of conflict between Israel and the militant Palestinian group Hamas in Gaza is escalating and could destabilize the Middle East. Britain urged its nationals to leave Lebanon and said it was moving 700 troops to Cyprus to help its citizens evacuate.

The UN Security Council said it would meet on Wednesday to discuss the conflict.

"Lebanon is at the brink. The people of Lebanon, the people of Israel, and the people of the world cannot afford Lebanon to become another Gaza," UN Secretary General Antonio Guterres said.

At the UN, which is holding its General Assembly this week, U.S. President Joe Biden made a plea for calm. "Full-scale war is not in anyone's interest. Even if a situation has escalated, a diplomatic solution is still possible," he said.

Lebanese Foreign Minister Abdallah Bou Habib criticized Biden's address as "not strong, not promising" and said the U.S. was the only country "that can really make a difference in the Middle East and with regard to Lebanon." Washington is Israel's longtime ally and biggest arms supplier.

The United States "is the key ... to our salvation," he told an event in New York City hosted by the Carnegie Endowment for International Peace.

In Beirut, thousands of displaced people who fled from southern Lebanon were sheltering in schools and other buildings.

At the Technical Institute of Bir Hassan, volunteers brought water bottles, medicine and other supplies for the new arrivals.

In one classroom, 11-month-old Matila slept on a mattress while children elsewhere stood on chairs to pass time by scribbling on a whiteboard. Rima Ali Chahine, 50, said the shelter provided diapers, pastries and milk for the children.

"It's a lot of pressure for grownups and children. They're exhausted and stressed. They could not sleep," she said. "The kids – they are living through terrible conditions."

Early on Wednesday, an Israeli strike hit the seaside town of Jiyyeh, 75 kilometers north of the border with Israel, two security sources said.

Half a million people are estimated to have been displaced in Lebanon, said Bou Habib. He said Lebanon's prime minister hoped to meet with U.S. officials over the next two days.

The U.S. and fellow mediators Qatar and Egypt have so far been unsuccessful in their efforts to negotiate a ceasefire in the nearly year-old war in Gaza between Israel and Hamas, a Hezbollah ally.