International mediators are drawing up a new attempt to bridge the remaining gaps between Israel and Hamas on a Gaza cease-fire, according to U.S. and Arab officials, even as Prime Minister Benjamin Netanyahu of Israel has doubled down on his country’s control of Gaza’s border with Egypt, a key stumbling block.

The officials spoke on condition of anonymity to discuss the negotiations, as the latest proposals have yet to be finalized. Israeli officials and Hamas leaders have expressed pessimism over the prospects for an agreement, despite rising public fury in Israel over the failure to bring home the remaining hostages held in Gaza.

More than 60 living hostages, and the bodies of about 35 other hostages believed to be dead, are still in Gaza, according to the Israeli authorities.

Mass protests erupted in Israel this week after the bodies of six Israeli hostages were found in Gaza; all of them had recently been executed by Hamas, according to Israel. Hamas has issued mixed statements, but at least one heavily implied that the hostages were killed because their captors understood Israeli troops were nearby.

For months, mediators from Egypt, Qatar and the United States have sought to broker an agreement between Hamas and Israel to end the war in Gaza and free the hostages. Two rounds of high-level negotiations last month in Cairo and in Doha ended without a breakthrough.

But Mr. Netanyahu has stuck to his position that Israel must retain control of Gaza’s border with Egypt — known as the Philadelphi Corridor — to prevent Hamas from rearming itself, even at the cost of reaching a deal to free the more than 100 remaining hostages.

“It will determine our entire future,” Mr. Netanyahu told reporters as protesters demanding an immediate cease-fire to free the hostages demonstrated outside his Jerusalem home.

“On this we must all be insistent, otherwise we will receive all of this disaster again,” he added, referring to the Hamas-led Oct. 7 attack on southern Israel that prompted the war in Gaza.

Hamas has repeatedly said that any cease-fire agreement must lead to a complete Israeli withdrawal from the Gaza Strip. Egypt has also voiced stiff opposition to a long-term Israeli presence along their border with Gaza.

“Without withdrawing from the Philadelphi Corridor, there will be no agreement,” Khalil al-Hayya, Hamas’s lead negotiator, told the Pan-Arab broadcaster Al Jazeera this week.

An Arab official, who spoke on condition of anonymity to discuss the sensitive talks, said Mr. Netanyahu’s insistence on maintaining Israeli control of the Philadelphi Corridor now posed the main obstacle to an agreement.