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.

Egyptian and Israeli officials will hold talks in Cairo on Sunday to discuss the reopening the Rafah border crossing between Gaza and Egypt, an Egyptian security official confirmed to ABC News.

The crossing has been closed since Israeli forces took control of the Gaza side during their offensive toward Rafah in May. Egyptian officials have said they will not reopen the crossing as long as Israel controls the Gaza side.

Egypt has, however, agreed to send aid trucks from its side of the border to be processed from the Israeli border checkpoint of Kerem Shalom.

-ABC News’ Ayat Al-Tawy

Although President Joe Biden on Friday outlined a multi-phase cease-fire proposal he said came from Israel, the Israeli Prime Minister’s Office said in a statement Saturday that "Israel's conditions for ending the war have not changed: the destruction of Hamas's military and governing capabilities, the freeing of all hostages and ensuring that Gaza no longer poses a threat to Israel."

"Under the proposal, Israel will continue to insist these conditions are met before a permanent cease-fire is put in place," the statement said. "The notion that Israel will agree to a permanent cease-fire before these conditions are fulfilled is a non-starter."

Biden said Friday that Israelis should feel comfortable with a cease-fire because Hamas’s capabilities have deteriorated and can no longer repeat the Oct. 7 terrorist attacks.

Hamas in a statement reiterated its requirements for a deal. Hamas said it "affirms its position of readiness to deal positively and constructively with any proposal based on a permanent cease-fire, complete withdrawal from the Gaza Strip, reconstruction, the return of the displaced to all their places of residence, and the completion of a serious prisoner exchange deal."