After Mr. Lieberman quit, the education minister, Mr. Bennett, demanded that he be named defense minister; he was rebuffed by the prime minister on Friday. The Jewish Home party had threatened to quit the coalition if Mr. Bennett, who has espoused far more belligerent positions on security than Mr. Netanyahu, did not get the job.
In a high-stakes move, Mr. Bennett and his colleague Ayelet Shaked, the justice minister, also from Jewish Home, announced on Sunday night that they would be making a statement on Monday morning. Even people in their own party said the expectation was that they would resign.
In the end, perhaps heedful of Mr. Netanyahu’s warnings against bringing down one of the most right-wing governments Israel has known, a move that could have had unpredictable consequences, they backed down.
Mr. Bennett and Ms. Shaked presented their reversal as a result of their dedication to the national interest.
“It is possible to change direction,” Mr. Bennett said. He added that he hoped Mr. Netanyahu was serious when he hinted on Sunday that Israel was planning stronger military action in Gaza.
Ms. Shaked said Jewish Home would “continue to be the national compass of this government,” adding, in a dig at Mr. Lieberman, “We will not flee from responsibility.”
Ofir Akunis, a Likud minister, enumerated on Monday some of the security, economic and diplomatic challenges ahead. “Soon the American president will present his ‘deal of the century,’ ” he told Israel Radio, referring to Mr. Trump’s peace proposal, “and this will be a huge challenge, primarily for the right wing, because it is liable to contain the two states for two peoples formula, and we must fight this, from inside the government.”