The UN chief warned world leaders on Tuesday that Lebanon was on "the brink" as Israel intensifies attacks across the country, killing over 500 people - 50 of them children - in less than 48 hours.
The gathering of dozens of world leaders, the high point of the diplomatic calendar, comes as Biden marks his last appearance at the UN General Assembly.
"We should all be alarmed by the escalation. Lebanon is at the brink," UN Secretary-General Antonio Guterres said.
As world leaders gathered in Manhattan for the annual flurry of speeches and face-to-face diplomacy, UN Security Council member France called on Monday for an emergency meeting on the crisis engulfing the Middle East.
As the toll in Lebanon climbed, focus shifted away from the situation in Gaza, and the EU's top diplomat Josep Borrell warned "we are almost in a full-fledged war."
The United States, Israel's closest ally, again warned against a full-blown ground invasion of Lebanon, with a senior US official promising to bring "concrete" ideas for de-escalation to the UN this week.
It is unclear what progress can be made to defuse the situation in Lebanon as efforts to broker a ceasefire in Gaza, which Israel has relentlessly pounded since October 2023, have come to nothing.
Guterres cautioned against "the possibility of transforming Lebanon (into) another Gaza."
Richard Gowan of the International Crisis Group think tank said he expected many leaders to "warn that the UN will become irrelevant globally if it cannot help make peace."
More than 100 heads of state and government are scheduled to speak during the UN's centerpiece event, which will run until Monday.
Since last year's annual gathering, when Sudan's civil war and Russia's Ukraine invasion dominated, the world has faced an explosion of crises.
"International challenges are moving faster than our ability to solve them," Guterres warned ahead of the gathering.
The October 7 attack by Palestinian Islamist group Hamas on Israel and the ensuing violence in the Middle East has exposed deep divisions in the global body.
With Israel's leader Benjamin Netanyahu and Palestinian president Mahmud Abbas expected to address the General Assembly this week, there could be combustible moments.
On Tuesday, representatives of Turkey, Jordan, Qatar, Iran and Algeria are slated to take the podium to press for a Gaza ceasefire after nearly one year of war.
Ukraine will also be on the agenda Tuesday when President Volodymyr Zelensky addresses a UN Security Council meeting on Russia's war on Ukraine.
"I invite all leaders and nations to continue supporting our joint efforts for a just and peaceful future," Zelensky told the UN on Monday.
"Putin has stolen much already, but he will never steal the world's future."
It is unclear if the grand diplomatic gathering can achieve anything for the millions mired in conflict and poverty globally.
"Any real diplomacy to reduce tensions will take place behind the scenes," Gowan said.
"This may be an opportunity for Western and Arab diplomats to have some quiet conversations with the Iranians about the need to stop the regional situation spinning out of control."
Iraqi Prime Minister Mohammed Shia al-Sudani has called for an urgent meeting of Arab leaders on the sidelines of the UN General Assembly over the crisis in Lebanon.
Guterres cautioned against "the possibility of transforming Lebanon (into) another Gaza."