But even some of Mr. Gantz’s supporters balk at teaming up with Arab politicians, saying that a state established to protect the Jewish people, and still in conflict with the Palestinians, cannot entrust weighty policy decisions to people whose sympathies may be with the other side.

The roiling debate, which has set back the effort to depose Mr. Netanyahu and could force Israel to hold a record fourth election, turns on a question at the heart of the country’s existence as a democratic and Jewish state:

Are the votes of Arab citizens worth as much as those of Jews?

Arab citizens make up a fifth of Israel’s population and for the first time have come close to proportional representation in Parliament. The predominantly Arab Joint List won nearly 582,000 votes and a record 15 parliamentary seats, enough to be decisive in an election in which neither Mr. Netanyahu’s bloc nor Mr. Gantz’s won a majority.

But Mr. Netanyahu declared those votes “not part of the equation.” The Joint List, he said, “attacks our soldiers and opposes the State of Israel.”

Critics said his dismissal of the Arab vote was not only self-serving — the 15 seats combined with Mr. Gantz’s coalition would boot Mr. Netanyahu from office — but also racist and antidemocratic.

“Dismissing more than half a million citizens by rendering the 15 members of the Joint List illegitimate, coupled with incitement against anyone who engages with them, crosses a red line,” Yuval Diskin, a former head of the internal security agency, wrote Wednesday in Yediot Ahronot.