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

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.

The foreign ministers of the Group of 7 said they have "deep concern" over "the trend of escalatory violence" in the Middle East, in a joint statement Tuesday.

The statement doesn’t call out Israel by name, it does call for "a stop to the current destructive cycle," warning "no country stands to gain from a further escalation in the Middle East."

"Actions and counter-reactions risk magnifying this dangerous spiral of violence and dragging the entire Middle East into a broader regional conflict with unimaginable consequences," it reads, while calling for the full implementation of the U.N. Security Council resolution that implemented a cease-fire between Israel and Hezbollah in 2006.

Additionally, the statement reaffirms the G7’s "strong support" for the ongoing efforts to broker a hostage release and cease-fire deal in Gaza.