Prime Minister Benjamin Netanyahu, acting through coalition chairman Ze'ev Elkin, invited all parties except the Arab parties and the Hadash party to join the coalition on Tuesday evening.
Several faction leaders rejected the offer and others said they would respond on Wednesday.
The prime minister stressed the need for national unity in a televised address earlier on Tuesday, following an attack on a Jerusalem synagogue by two Palestinian assailants, which killed four and wounded several others.
Opposition leader and Labor chairman MK Isaac Herzog refused the offer, saying that while unity is important, especially at this time, "the Labor party will not be part of a government whose policy doesn't give security and hope to Israeli citizens."
"The Labor party is an ideological and political alternative and should be at the helm of the state's leadership, because a change is needed here, and quickly. It has nothing to look for in a government led by Netanyahu and Likud," Herzog said.
Meretz also rejected the offer. Meretz Chairwoman Zahava Gal-On said unity cannot be a reason to "lend a hand to a government which only adds fuel to the fire, blocking every way to put an end to the hostility and violence." Gal-On also slammed Netanyahu's effort at a wider coalition, saying it is an exploitation of the Jerusalem attack for "cynical, political wheeling and dealing."
"If the prime minister heads for a diplomatic process which requires true compromise, Meretz will give him a safety net," she said.
At the same time, Netanyahu also called on his fellows to the coalition to put their serious divides behind them and resume cooperation at the cabinet.
On Monday, Netanyahu reportedly told top Likud officials Monday to get ready for a possible early election. Indicating he sees an early election as a last resort, Netanyahu told the top Likud officials: “Prepare for early elections, in the hope that we won’t get there.”
Monday, Netanyahu canceled a meeting aimed at examining the possibility of early elections and discussing reports that Finance Minister Yair Lapid was planning to ditch the prime minister and form an “alternative coalition.”
Netanyahu told senior Likud officials he was concerned the coalition would collapse shortly due to the ongoing dispute with Lapid, who heads the Yesh Atid party. A party official told Netanyahu that Likud was not ready to face an election, and suggested waiting until at least January.
Netanyahu associates said his bureau renewed talks with Lapid Monday in an effort to reach a compromise that would allow the budget to be passed soon.
At least four party heads have been invited to join a theoretical coalition headed by Lapid, Likud officials said. Ultra-Orthodox MKs said Lapid and opposition leader Isaac Herzog of Labor have asked them to consider joining a coalition they would lead.
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