As U.S. Secretary of State Antony Blinken continues his meetings with Middle Eastern mediators working toward a Gaza cease-fire deal, a senior U.S. official traveling with his delegation is criticizing comments about the process emanating from both Israel and Hamas, casting them as unproductive.

The official, who spoke on the condition of anonymity, addressed reports that Israeli Prime Minister Benjamin Netanyahu took a hawkish stance in a meeting with hostage families, telling them he was "unsure" there would be an agreement to return those held captive in Gaza and that he would not withdraw troops from strategic areas of the enclave -- a key sticking point in negotiations.

"Maximalist statements like this are not constructive to getting a cease-fire deal across the finish lines," the official said. "And they certainly risk the ability of implementing and working level and technical talks to be able to move forward when both parties agree to a bridging proposal."

The senior official also dismissed Hamas’ latest statement accusing the U.S. of "blind bias towards Israel."

"They say a lot of things and they do a lot of different things," the official said, suggesting the militant group’s ongoing engagement was an indication that Hamas was still involved in the negotiation process despite its insistences to the contrary.

-ABC News' Shannon K. Kingston

Israeli forces have identified over 115 projectiles crossing from Lebanon into northern Israel on Tuesday, the IDF said.

Hezbollah has also released statements about eight different attacks on northern Israel Tuesday.

Two people were killed after Israeli strikes on the town of Al-Dhahira Tuesday, the Lebanese Ministry of Public Health said.

-ABC News' Jordana Miller and Ghazi Balkiz

At least 12 people have been killed in another strike on a school in the Gaza Strip where displaced people were sheltering, the Gaza Civil Defense said Tuesday.

The Mustafa Khaft school in western Gaza City was hit by the Israeli air force, Israel confirmed in a statement, alleging that Hamas was using the facility as a command center.

"The command and control center was embedded and hidden by the Hamas terrorist organization inside," the IDF statement said. "Hamas terrorists used the command and control center to plan and execute attacks against IDF troops and the state of Israel."

The IDF said it took "numerous steps" to mitigate the risk of harming civilians, "including the use of precise munitions, aerial surveillance and additional intelligence."

A number of people are still missing after the strike, according to the Gaza Civil Defense. Around 700 people were sheltering in the school, according to Palestinian officials.

Israeli forces have repeatedly targeted Gaza schools -- some of which are doubling as shelters for people displaced by the fierce fighting -- they say are being used as Hamas military hubs and weapon storage sites.

Earlier this month, the U.N. Human Rights Office accused Israel of "systematic attacks" on schools following a strike on the Al Tabae'en School in Gaza City.

-ABC News' Sami Zayara and Joe Simonetti

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