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.

- View from Israel -

Israeli warplanes pounded villages in south Lebanon for a third day, Lebanese media reported Wednesday, while Israel said it intercepted a missile fired after sirens sounded early morning in Tel Aviv.

Lebanese officials said hundreds of thousands of civilians have fled their homes in the south this week to avoid fighting between Hezbollah and the Israeli military.

Lebanon's official National News Agency said Israeli warplanes launched raids on multiple towns in the south from 5:00 am (0200 GMT), adding "casualties were reported" from other strikes overnight.

Israel's military campaign to eradicate Hamas in retaliation for the October 7 attack has weakened it by killing several of its leaders and thousands of fighters, and by reducing swaths of the territory it rules to rubble.

But the Palestinian militant group has not been crushed outright, and a year on from its unprecedented attack on Israel, an end to its hold over Gaza remains elusive.

Hamas sparked the Gaza war by sending hundreds of fighters across the border into Israel on October 7, 2023, to attack communities in the south.

Nearly a year of war in Gaza has battered Israel's economy, and poverty is now threatening communities including in areas far removed from the fighting against Hamas.

Mass protests against Prime Minister Benjamin Netanyahu's controversial judicial reforms had already weakened Israel's economy prior to the Hamas attack on October 7.

But it was dealt a major blow by the impact of the worst attack in its history, and the war that has followed.

A year after October 7, Israelis are united in the trauma caused by Hamas's attack on their country, but are divided in their views on how to end the war.

In the aftermath of the attack, the deadliest in Israeli history, a movement of national solidarity emerged, with volunteers preparing meals for soldiers and welcoming displaced people into their homes.

This shared grief and solidarity offered Israelis some comfort, but the health ministry says that the country now faces "the most serious mental health crisis in its history".

World leaders lined up at the United Nations on Tuesday to call on Israel to refrain from a full-scale war in Lebanon, with the organization's chief warning the situation was on the "brink."

The UN General Assembly, the high point of the international diplomatic calendar, comes after Lebanese authorities said Israeli strikes had killed 558 people -- 50 of them children.

"Full-scale war is not in anyone's interest. Even though the situation has escalated, a diplomatic solution is still possible," US President Joe Biden said in his farewell address to the global body.

Joe Biden gave a somber farewell address to the United Nations on Tuesday, using his own decision to drop out of the US presidential election to warn of the dangers of autocrats around the globe refusing to quit.

"My fellow leaders, let us never forget -- some things are more important than staying in power," Biden said to applause in his final speech at the UN General Assembly in New York.

The 81-year-old exhorted world leaders to stand up for democracy in the face of spiraling turmoil and conflict, urging support for Ukraine and pushing for peace in the Middle East.

For nearly a year, one of US President Joe Biden's top priorities has been to prevent the Gaza war from spiraling into an all-out regional conflict.

Weeks ahead of an election -- and just as Biden begins his farewell visit to the UN General Assembly -- Israel is pounding Lebanon, killing hundreds and highlighting the powerlessness of his warnings.

Biden, meeting the leader of the United Arab Emirates on Monday, insisted that his administration was still "working to de-escalate" in coordination with counterparts.

US President Joe Biden met UAE President Sheikh Mohamed bin Zayed Al Nahyan on Monday for talks on conflicts in the Middle East and Sudan -- despite concerns over the Gulf power's own role in the Sudan conflict.

Democratic presidential nominee Kamala Harris also met the Emirati leader at the White House, the first ever visit in Washington by a president of the oil-rich monarchy.

In a joint statement after their meeting, Biden and Sheikh Mohamed said they "shared concern about the risk of imminent atrocities" as fighting continues in Sudan's war-torn Darfur region.

As wars rage worldwide, with civilian casualties a daily occurrence, critics of the United Nations say the body is failing at its most basic job, while experts warn the organization is being scapegoated for things that are beyond its control.

Maintaining peace and international security is one of the UN's central missions, but its record has been badly tarnished as bloodshed intensifies in conflicts across the world, including in Gaza, Ukraine and Sudan.