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.

President Joe Biden outlined Israel’s cease-fire proposal accurately in his Friday speech, the White House maintained Monday, pushing back on suggestions he miscommunicated the offer.

"The Israeli foreign minister himself acknowledged that this was the Israeli proposal ... and we're confident that it accurately reflects that proposal, a proposal that we worked with the Israelis on," White House national security communications adviser John Kirby told reporters.

Kirby also argued that Biden "felt it was important" to reveal details from ongoing cease-fire negotiations for the first time, saying it was meant to apply pressure on Hamas, not to corner Israeli Prime Minister Benjamin Netanyahu.

"We don't typically go through the details of these kinds of proposals," Kirby said. "But in this case, given where we are, given how much longer the hostages have now been held, given the fact that Hamas has reneged on several past occasions, on proposals that were sent to them, and given the fact that the Israelis really did work hard to come up with this proposal, and did so in good faith, the president felt it was important for the first time to publicly lay that out."

"This wasn't about jamming the prime minister or the war cabinet," Kirby added. "This was about laying bare for the public to see how well and how faithfully and how assertively the Israelis came up with a new proposal, how it shows how much they really want to get this done."

Kirby said Biden delivered the speech on Friday afternoon because the deal was presented to Hamas the night before.

"We're awaiting an official response by them now to take the deal," Kirby said. "This gives them what they've been looking for, which is a cease-fire and over time, and through the phases, the potential withdrawal of Israeli forces from Gaza."

-ABC News’ Fritz Farrow