NEW YORK – President Joe Biden’s administration headed into the annual U.N. General Assembly gathering of world leaders this week with high hopes that he could cement his legacy as an international statesman during escalating conflicts in the Middle East and Ukraine.

Yet five days of frantic diplomacy focused mainly on preventing the Israel-Hezbollah crisis from exploding into a full-scale war has yielded little, if any, results — and prospects for peace have further dimmed.

Despite a proposal from the U.S., France and other allies for a temporary cease-fire along the border with Lebanon, Israeli Prime Minister Benjamin Netanyahu delivered a defiant speech Friday to the General Assembly, vowing to keep up operations against Hezbollah until tens of thousands of Israeli citizens displaced by rocket attacks can return home.

As Netanyahu spoke, Israel launched a massive strike on Hezbollah’s main headquarters in Beirut. He then cut his already-truncated visit to New York short and was poised to head home without plans to meet senior U.S. officials.

Netanyahu’s speech and his abbreviated trip — without seeing anyone from Israel’s largest and most important backer, the United States — underscored the limits of American influence, which many believe has been waning since Israel’s war with Hamas, another Iranian-backed militant group, began nearly a year ago.

“If we’re able to get the cease-fire in the north, that may create some space and maybe even some momentum to try to get the Gaza cease-fire, the Gaza hostage deal, over the finish line,” Secretary of State Antony Blinken told MSNBC on Thursday.

This week began with Biden’s top national security aides working to build support for a 21-day Israel-Hezbollah cease-fire that they hoped might also breathe new life into stalled efforts to secure a truce in Gaza.

After three days of intense talks with partners and allies — punctuated by a brief spat between the United States and France over the timing — the proposal was presented late Wednesday.

The Americans were particularly perturbed by France calling an emergency U.N. Security Council session on Lebanon for Wednesday evening — at which the French foreign minister previewed the as-yet unfinished proposal — while at the same time Biden was hosting a reception for world leaders at the Metropolitan Museum of Art. That effectively forced the U.S. to unveil it before many officials believed it was ready.

Nearly four hours after that Security Council meeting began, the White House released the plan. U.S. officials then offered upbeat assessments of its prospects over the objections of some in the Biden administration who had urged caution, according to several people familiar with the negotiations who spoke on condition of anonymity to detail private discussions.

After consulting with senior Israeli officials, Blinken and other diplomats had expected Israel to at least welcome, if not endorse, the plan. Instead, Netanyahu appeared to reject it when he arrived in New York on Thursday. He later clarified that Israel supports the goals of the cease-fire.

But in his U.N. speech, the Israeli leader castigated much of the world for trying to push his country into accepting an untenable situation along its northern border.

“We’ll continue degrading Hezbollah until all our objectives are met,” he told the General Assembly on Friday, just before reports emerged that Israeli had struck Hezbollah’s headquarters. “I’ve come here today to say: Enough is enough.”