Israel-Gaza live updates: Sirens sound in Tel Aviv as Hamas fires rocket from Gaza

The bodies of six Israeli hostages were recovered in an overnight operation inside the Gaza Strip.

The six men were found in a tunnel in the southern city of Khan Younis during a joint Israel Defense Forces and Israel Security Agency -- also known as Shin Bet -- operation.

The hostages are Alex Dancyg, 75, Yagev Buchshtav, 35, Chaim Peri, 79, Yoram Metzger, 80, Nadav Popplewell, 51, and Avraham Munder, 78.

All had been declared dead before their bodies were recovered. The cause of their deaths has not been revealed. Funerals are expected for some of the dead later on Tuesday.

-ABC News’ Joe Simonetti

Senior Hamas official Osama Hamdan said that Israeli Prime Minister Benjamin Netanyahu's talk about approving an updated proposal means that the U.S. administration failed to convince Netanyahu of the previous deal that Hamas had already agreed to back on July 2.

Hamdan made the comments during an interview with Al Jazeera on Monday evening local time after Blinken's meeting with Netanyahu in Israel and announcement that Netanyahu had voiced support for the U.S.-backed bridging proposal.

Hamdan said that all the U.S. side is doing is buying time for Israel to "continue its crimes of genocide."

-ABC News’ Nasser Atta and Guy Davies

Freed Israeli hostage Aviva Siegel, whose husband Keith is still held captive, said she was feeling "happier and more optimistic than before" after meeting with U.S. Secretary of State Antony Blinken on Tuesday. After hearing from Blinken, Siegel said she wants to believe that her husband, an American-Israeli citizen, will be home soon.

Siegel said Blinken gave her the impression that Israeli Prime Minister Benjamin Netanyahu wants the deal that's on the table, but cautioned that it sounds like hard work needs to be done to close the gaps with Hamas.

Outside of the building where families of the hostages met Blinken, crowds chanted "SOS USA" and waved American flags, with a message to Blinken that the U.S. government is their main lifeline to bring the hostages home.

Despite the optimism from the Biden administration, momentum appears to have slowed. Talks in Doha did not end with any major breakthrough, and a U.S.-presented "bridging proposal" has been dismissed by Hamas, who accuse Netanyahu of adding new conditions and obstacles, including the rejection of a permanent ceasefire.

Blinken travels to Egypt tomorrow, where he says he'll get the latest from Egyptian and Qatari leaders on Hamas' intentions.

-ABC News' Britt Clennett, Guy Davies, Anna Burd and Tomer Slutzky

At least eight people have been injured from Israeli strikes on the Beqaa Valley, the Lebanese Ministry of Public Health said Monday.

Among the wounded are six Lebanese citizens, a 5-year-old Syrian girl and a 15-year-old Syrian girl. All of them were treated in the emergency room at nearby hospitals, the Ministry of Public Health said.

There were seven Israeli strikes in southern Lebanon on Monday, according to Lebanese local media.

In two separate statements Monday, the IDF acknowledged conducting operations "in the area of Houla in southern Lebanon," "in the area of Beqaa in Lebanon" and in “the area of Tayibe in southern Lebanon.”

-ABC News’ Ghazi Balkiz