Israel-Gaza-Lebanon updates: Nasrallah killed for tying Hezbollah cause to Gaza war

The number of people displaced in southern Lebanon as a result of Israeli airstrikes may be approaching half a million, according to Lebanese Foreign Minister Bou Habib, who stressed that "the war in Lebanon will not help the Israelis return to their homes, and negotiations are the only way to do so."

Habib spoke at an event hosted by the Carnegie Endowment for International Peace on Tuesday while attending the United Nations General Assembly.

He expressed his "disappointment" over U.S. President Joe Biden’s speech at the U.N., saying it was "neither strong nor promising and will not solve this problem," but said he "hopes that Washington can intervene to help."

"Lebanon cannot end the fighting alone and needs America's help, despite past disappointments," Habib said, adding that the U.S. is "the only country that can truly make a difference in the Middle East and with regard to Lebanon."

-ABC News' William Gretsky

Mediators between Israel and Hamas are as far away from a cease-fire deal as they have ever been, with both sides impeding negotiations, multiple senior U.S. officials told ABC News.

Many officials have long been skeptical that Hamas leader Yahya Sinwar would ever sign off on an agreement that involves ceding rule of Gaza, and in recent weeks Hamas has deeply frustrated the Israeli government by adding demands related to Palestinian prisoners that would be released in an exchange.

Israel Prime Minister Benjamin Netanyahu has also become increasingly intractable, according to U.S. officials. While high-level engagements between the U.S. and Israel often moved the needle at the beginning of the conflict, those meetings are now unproductive, officials said -- a major reason Secretary of State Antony Blinken didn't stop in Israel during his last visit to Middle East.

When it comes to these negotiations, the ball is actually in the Biden administration’s court. Blinken promised during the first week of September that the U.S. would present a new, final proposal to both Israel and Hamas "in the coming days," but almost three weeks later, there’s no indication that has happened yet.

The reason for the delay is the struggle to devise an arrangement both sides might agree to -- but that's just one more factor contributing to the gridlock, according to U.S. officials.

-ABC News' Cindy Smith, Shannon K. Kingston and Martha Raddatz

Hezbollah fired over 300 rockets, missiles and drones on Israel on Tuesday, injuring six soldiers and civilians in Israel, according to officials.

The group tried to fire many more strikes that were disrupted, according to IDF spokesperson Daniel Hagari.

Israel said Hezbollah has many capabilities it knows about and is going after, now targeting the threats at the border, according to Hagari.

Hagari said Hezbollah has militarized southern Lebanon and placed missiles and rockets in thousands of homes.

Asked if Hezbollah head Hassan Nasrallah is a target, Hagari pointed to comments from IDF General Staff Rav Aluf Herzi Halevi, who previously said no one in Hezbollah is immune.

Israel has "additional strikes prepared" against Hezbollah, Defense Minister Yoav Gallant said, in a discussion with troops on Tuesday.

"Hezbollah, today, is different from the organization we knew a week ago – and we have additional strikes prepared. Any Hezbollah force that you may encounter, will be destroyed. They are worried about the combat experience you have gained," Gallant said.