Mr. Netanyahu and Mr. Bennett plan to finalize details of their agreement and sign it Thursday, and the new government is slated to be sworn in next week. Some details remain unclear, but the Likud-led coalition will include Kulanu, a new center-right faction focused on the economy; two ultra-Orthodox parties, United Torah Judaism and Shas; and the Jewish Home, which favors expanding settlements in the occupied West Bank and opposes the establishment of a Palestinian state.

Mr. Bennett is expected to serve as education minister, and another Jewish Home member, Ayelet Shaked, as justice minister; both will probably sit in the security cabinet, which makes critical decisions about war and peace. Kulanu’s leader, Moshe Kahlon, a former Likud minister, will become finance minister and will also serve in the security cabinet, along with Moshe Ya’alon of Likud, who is likely to continue as defense minister. Mr. Netanyahu himself will probably double as foreign minister for now.

Mr. Netanyahu’s comments, and statements earlier Wednesday by other Likud leaders, suggested that he would soon try to lure Isaac Herzog of the center-left Zionist Union as foreign minister in a national unity government. But Mr. Herzog denounced Wednesday night’s deal as “a government of national failure.”

On Twitter, Mr. Herzog called it a “government with no responsibility, stability or governance,” and on Facebook, he said it was “the most weak, narrow and squeezable government in Israel’s history.”

With Mr. Lieberman’s late-in-the-game withdrawal, Mr. Bennett used his added leverage to demand the Justice Ministry for Ms. Shaked, stirring outrage. She is an outspoken hawk on the Palestinian issue who has described African asylum-seekers as a threat to Israel’s Jewish character and has pressed for a “nationality bill” that critics say would disenfranchise Arab citizens.

Nachman Shai, a Zionist Union lawmaker, said giving Ms. Shaked the post “would be like appointing a pyromaniac to head the fire department.” Mouin Rabbani, a senior fellow at the Institute for Palestine Studies, called the new Israeli government “the most extremist in its history.”

“Since this government does not pay even lip service to the charade of a negotiated peace with the Palestinians, the international community and Western powers in particular can dispense with the traditional honeymoon period,” Mr. Rabbani said in a statement circulated by the Washington-based Institute for Middle East Understanding. “If there is to be any hope for peace in the Middle East, it needs to begin with an end to Israeli impunity and by holding this government to account for its actions.”