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“I hope that we will be able to return to proper conduct. This is what the public expects of us because only thus is it possible to run the country, and if not, we will draw conclusions.”

His comments were the clearest sign yet that the country was heading toward an early election, less than two years after Mr. Netanyahu formed a mostly right-wing coalition in which Mr. Lapid headed the second-biggest party.

The combative Mr. Netanyahu has faced falling approval ratings but opinion surveys indicate that Likud would again emerge as the largest party in a fresh poll, giving him a fourth term as premier. After days of talk of a “coalition crisis,” sources close to the Israeli leader said the country was “98% into an election,” the liberal newspaper Haaretz reported.

The open talk of an election followed threats from Tzipi Livni, the justice minister, and Mr. Lapid to resign if a controversial bill to declare Israel “the nation state of the Jewish people” became law.

Although its 1948 Declaration of Independence already does this, critics say enshrining it in law would undermine Israel’s democratic character, enrage the country’s Arab minority, and possibly enable future illiberal legislation.

The prime minister says the law is necessary to fend off Palestinian opposition to Jews’ right to live in Israel, but Mr. Lapid and Ms. Livni say it is a threat to the country’s democratic character since it would reduce Arabs to second-class citizenship, and that it has been introduced for electioneering purposes.