Sec. of State Anthony Blinken spoke to Israeli Defense Minister Yoav Gallant on Sunday about the proposal for a ceasefire-hostage deal.

The deal would secure the release of the hostages and ensure a surge in humanitarian assistance throughout Gaza.

"The Secretary commended Israel’s readiness to conclude a deal and affirmed that the onus is on Hamas to accept," according to a readout of the call.

During the call, Blinken also reaffirmed America's commitment to Israel's security.

In a joint statement shared by the U.S. State Department on Saturday, mediators from the U.S., Egypt and Qatar said they’re working to secure a cease-fire in Gaza and the release of the hostages, and urged Hamas and Israel "to finalize the agreement" that President Joe Biden outlined on Friday.

"These principles brought the demands of all parties together in a deal that serves multiple interests and will bring immediate relief both to the long-suffering people of Gaza as well as the long-suffering hostages and their families," the statement said. "This deal offers a roadmap for a permanent ceasefire and ending the crisis."

An Israeli government official said the Israeli Prime Minister’s Office wasn’t informed that President Joe Biden’s Friday remarks would include a permanent end to the fighting.

“If you listen to what Biden said, you come to the impression that we agree to a permanent cease-fire without, or, without our conditions being met, and that's not the case,” the official said.

The official said the Israeli Prime Minister’s Office, including Prime Minister Benjamin Netanyahu, was informed 30 minutes before that Biden was giving a speech. The official said Netanyahu was told that the speech would focus on the hostages, with no mention of implementing a permanent cease-fire.

A senior U.S. official said the Biden administration "engaged with the Israelis at multiple levels before the president delivered the speech." The official said the U.S. specifically engaged with the Israeli Prime Minister's Office and the Israeli war cabinet.

The official also pointed to when Biden said in his speech that it was a proposal that the Israelis agreed to. The official noted that Netanyahu himself said that it was an Israeli proposal.

An Israeli official and two other Israeli sources who are familiar with the matter told ABC News that what Biden presented is indeed the outline of the Israeli proposal. The sources said the proposal was approved by all war cabinet members, including Netanyahu, and sent to the mediators earlier in the week.

The sources added that there are “interpretation gaps,” referring to the way the outline was presented by Biden.

Biden presented on Friday what he said was an Israeli proposal to draw the war in Gaza to a close.

Biden said the deal had been transmitted to Israel and Hamas, through Qatar.

The president said the first phase would last for six weeks and include a "full and complete cease-fire, a withdrawal of Israeli forces from all populated areas of Gaza [and] release of a number of hostages." Palestinians would also be able to return to their homes and 600 trucks of humanitarian aid would be delivered to Gaza every day.

The second phase would include a release of all remaining living hostages and the temporary cease-fire would become a permanent cease-fire with Israel withdrawing all forces from Gaza "as long as Hamas lives up to its commitments," Biden said.

In phase three, there would be a major reconstruction of Gaza.

-ABC News’ Britt Clennett, Dana Savir and Michelle Stoddart

Right-wing Israeli Ministers Bezalel Smotrich and Itamar Ben Gvir spoke out on social media Saturday, both threatening to leave the government if the deal in its current form is accepted.

"I have now spoken with the Prime Minister and made it clear to him that I will not be part of a government that will agree to the proposed outline and end the war without destroying Hamas and returning all the abductees," Smotrich wrote.

This comes after the Hostage Families group released a statement urging Israel's parliament to embrace the deal.

Israeli forces confirmed the deaths of four more hostages: Haim Peri, Yoram Metzger, Amiram Cooper and Nadav Popplewell.

IDF spokesman Daniel Hagari said the four hostages were "killed together" a "few months ago" while "IDF forces were operating" in Khan Younis in southern Gaza. Hagari said Israeli forces are "examining the circumstances" of their deaths.

Cooper, 85, was an economist and a poet, and a father of four and grandfather of 11, according to Kibbutz Nir Oz. His wife, Nurit Cooper, was also kidnapped and later released, the kibbutz said.

Metzger, 80, was a father of three and grandfather of seven. His wife, Tamar Metzger, was also abducted to Gaza and later released, the kibbutz said.

Popplewell, 51, was kidnapped with his mother, who has been released, the Hostages Families Forum said.

Peri, 80, was abducted while protecting his wife, the Hostages Families Forum said. He leaves behind his wife, five children and 13 grandchildren.

Peri's family said he "heroically survived in the Hamas tunnels, under inhumane conditions, for around 4 months," and he "survived with the hope and faith that the state of Israel will fulfill its moral duty to bring him home."

"The government of Israel and its Prime Minister have no right to leave the hostages in captivity, dismantling Israel’s foundational principle of mutual responsibility," Peri's family said. "We call upon the government of Israel to strive for an immediate deal, save those still alive, and bring those who are not, to a proper burial."

"The heartbreak that comes with this painful news should shake every citizen in the State of Israel and lead every leader to profound soul-searching," the Hostages Families Forum said in a statement Monday. "The Israeli government must send out a negotiating delegation this evening and return all 124 hostages, both living and murdered. ... We reiterate our demand to the Israeli government: approve the Netanyahu deal immediately!"