In a speech timed to coincide with primetime news broadcasts on Sunday, Netanyahu stressed his long security background as he made the case for why he would keep the defense portfolio in his own hands, after the defense minister's resignation last week brought his government to the brink of collapse.
Education Minister Naftali Bennett said he would not quit the coalition government despite Netanyahu's refusal to name him as the new defense minister. He and Justice Minister Ayelet Shaked, also of Jewish Home, are set to deliver a statement to the media Monday.
Before his Sunday speech, Netanyahu met with Finance Minister Moshe Kahlon, who leads the center-right Kulanu party, which holds 10 seats in parliament.
Netanyahu is trying to convince them to stay, and his Likud allies are already preparing to pin the blame on them if that effort fails.
"I know I'll pay a political price - not the end of the world, you win some, you lose some", Bennett said.
But the release date is now likely to be influenced by the political crisis in Israel that has expected to spark early elections, Axios reported, citing unnamed US officials. Netanyahu said that Israel faces a very delicate and complex security situation and warned against bringing down the government.
On Wednesday, Defence Minister Avigdor Lieberman resigned over the ceasefire, throwing the government into crisis and leading to speculation that early elections had become inevitable.
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Kahlon's spokesman explained that the minister's position had not changed, and he still believes a one-seat majority destabilizes the coalition and leaves it open to extortion and "anti-fiscal bills" from backbenchers.
"I think that there is no reason to shorten the term of a national government, not even for one day, and at this moment it's in the hands of the education minister and the finance minister", said Gilad Erdan, the minister of public security.
When Jewish Home threatened to leave the government if Bennett was not appointed in Lieberman's place, early elections seemed nearly inevitable.
"We still have another year before elections; we are in the midst of the [national security] campaign and in the middle of a campaign you don't abandon it".
In a new violation of the Israel-Hamas ceasefire deal worked out by Egyptian mediators last week, a homemade military attack drone was discovered on Monday in a southern Israeli community near the Gaza border. Mr Bennett accepted that but called on Mr Netanyahu to be more right-wing in his leadership. When a truce was reached through United Nations and Egyptian mediation on Tuesday, Lieberman blasted the deal as "capitulation to terror" and quit.
According to Einat Wilf, a former member of the Knesset and fellow at the Washington Institute for Near East Policy, Mr Bennett fears that with the large overlap between their parties' bases, voters would have prioritised Mr Netanyahu's survival over strengthening Jewish Home. "We remember well what happened when elements inside the coalitions took down Likud governments in 1992 and in 1999", he said, noting the past two elections in which the Labor Party came to power. The country has always been eagerly awaiting the attorney general's decision on whether to press charges.