Secretary of State Antony Blinken arrived in Israel on Sunday for talks as part of the Biden administration’s push for a cease-fire in the 10-month-old conflict in Gaza that would include a prisoner exchange.

The Biden administration hopes a cease-fire in the Hamas war will lower tensions throughout the Middle East after a July 30 Israeli airstrike killed top Hezbollah official Fuad Shukr in Beirut and Hamas political chief Ismail Haniyeh was assassinated the next day in Tehran.

Hezbollah and Iran have vowed to retaliate.

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“Secretary Blinken will underscore the critical need for all parties in the region to avoid escalation or any other actions that could undermine the ability to finalize an agreement,” State Department spokesman Vedant Patel told reporters on Friday.

“This proposal would achieve a cease-fire in Gaza, secure the release of all hostages, ensure humanitarian assistance is distributed throughout Gaza, and create the conditions for broader regional stability,” Mr. Patel said.

President Biden sent Mr. Blinken to the Middle East to reaffirm his support for Israel’s security and continue efforts to finalize the agreement between both parties.

“With the cease-fire and hostage release deal now in sight, no one in the region should take actions to undermine this process,” Mr. Biden said Friday on X.

Even Israeli negotiators are said to have expressed “cautious optimism” over the possibility of a release of its hostages who were abducted by Hamas militants during their Oct. 7, 2023, attack into southern Israel that triggered the war.

Truce talks are expected to soon resume in Cairo following two days of negotiations in Doha last week.

Hamas put out an official statement rejecting the latest proposal discussed in Doha over the weekend, the Times of Israel reported Sunday.

The terror group blamed Israeli Prime Minister Benjamin Netanyahu for the impasse, saying he is putting up new obstacles in the talks.

Israel is insisting that Israel Defense Forces control the Philadelphi Corridor — a narrow strip of land running between Gaza and Egypt; the Rafah border crossing and the Netzarim Corridor that splits Gaza into a northern zone and a southern zone, Hamas said, according to the Times of Israel.

“The group also blames Netanyahu for introducing new conditions about the release of security prisoners,” the Times of Israel said.

Mr. Netanyahu said any pressure from the mediators of the ongoing negotiations should be leveled at Hamas, not Israel.

“Up until now, Hamas has been completely obstinate. It did not even send a representative to the talks in Doha,” Mr. Netanyahu said Sunday before a Cabinet meeting of Israeli government officials.

Israel is prepared for any threat and will defend itself against any attack even while they engage in negotiations for the release of their hostages, Mr. Netanyahu said.

“This is a national mission of the highest order. We are holding very complex negotiations in which the other side is a murderous terrorist organization that is unbridled and obstinate,” he said.

The Israeli delegation to the cease-fire talks knows which topics allow them room for flexibility and which require them to stand fast, Mr. Netanyahu said.

“We know how to distinguish between the two very well. We are conducting negotiations and not a scenario in which we just give and give,” he said. “Strong military and diplomatic pressure are the way to secure the release of our hostages.”