G7 nations have warned that "no country stands to gain from a further escalation in the Middle East," as world leaders gathered in New York for the annual U.N. General Assembly.

The relentless exchanges of fire between Israel and Lebanon's Hezbollah of recent days have stoked fears the longtime foes are moving inexorably towards all-out war, despite international appeals for restraint.

AFP correspondents in Jerusalem and Beirut talked to officials and analysts who told them what the opposing sides hope to achieve by ramping up their attacks and whether there is any way out.

Israeli Prime Minister Benjamin Netanyahu told Israel's security cabinet on Monday that Israel's aim in its military operations in Lebanon is to cut “Hezbollah from the war with Hamas,” an Israeli official told CNN.

The same official said the cabinet has agreed to continue to raise the level of military operations every day. Israel is aware of the risks, the source said, and is ready to stop at any moment. “It is up to Hezbollah,” the source said.

Qatar Airways and flydubai suspended flights to Beirut for two days on Tuesday as tensions escalated between Israel and Hezbollah after the deadliest bombardment of Lebanon since 2006.

Qatar Airways, the national flag-carrier which operates two flights a day to the Lebanese capital, cancelled services on Tuesday and Wednesday.

China's foreign ministry said on Tuesday it was "deeply shocked" by Israel's air strikes on Hezbollah strongholds in Lebanon after 492 people were killed in the deadliest bombardment since a devastating war in 2006.

"China... is deeply shocked by the relevant military actions that have caused large numbers of casualties," foreign ministry spokesman Lin Jian said in response to a question about Israel's strikes.

Hezbollah attacked Tuesday Kiryat Shmona in northern Israel with a salvo of rockets, "in defense of Lebanon," after the Israeli military hit dozens of targets in several areas of southern Lebanon overnight.

Hezbollah also fired overnight volleys of Fadi-1 and Fadi-2 rockets at the Megiddo military airport west of Israel's Afula, the Ramat David air base near Haifa, the Amos logistic base and the Zikhron explosives factory, 60 kilometers from the border.

Israeli air strikes on Lebanon killed at least 558 people on Monday, including 50 children, the health ministry said, marking the deadliest day of cross-border violence since the Gaza war began.

Arab states strongly condemned Israel for the escalating hostilities with Hezbollah, which have intensified to levels unseen in nearly a year.

The United States is presenting “concrete” ideas to ease the crisis in Lebanon, a U.S. official said, while voicing opposition to any Israeli ground invasion to target Hezbollah.

“We’ve got some concrete ideas we’re going to be discussing with allies and partners this week to try to figure out the way forward on this,” the senior U.S. official said as world leaders gathered in New York for the U.N. General Assembly.

The U.S. is sending additional troops to the Middle East in response to a sharp spike in violence between Israel and Hezbollah forces in Lebanon that has raised the risk of a greater regional war, the Pentagon said Monday.

Pentagon press secretary Maj. Gen. Pat Ryder would provide no details on how many additional forces or what they would be tasked to do. The U.S. currently has about 40,000 troops in the region.

President Joe Biden said on Monday that the United States was trying to calm the situation in Lebanon after Israeli air strikes on Hezbollah strongholds killed at least 274 people, including children.

"I've been briefed on the latest developments in Israel and Lebanon. My team is in constant contact with their counterparts, and we're working to de-escalate in a way that allows people to return home safely," Biden said as he held talks with UAE President Sheikh Mohamed bin Zayed Al Nahyan at the White House.