But he has done it, in large part, by irritating those same liberals. Whether by design or by accident, Mr. Gabbay keeps popping off in ways that appeal to the right, not to the left. He spurned the idea of a coalition with Arab parties in the Knesset, saying they represented the constituents of the Palestinian Authority leader Mahmoud Abbas, not Israeli Arabs. Mr. Gabbay welcomed a beefing up of religious content in public schools. He pooh-poohed the evacuation of West Bank settlements for the sake of peace with the Palestinians.
And he dusted off an old Netanyahu insult about how “the left has forgotten what it means to be Jewish.”
Mr. Gabbay now insists he was merely making a point about how to woo the more traditional Israelis who want to feel that they share the same values, not just policy views, with their leaders. “I respect everybody, whether they believe or don’t believe,” he said while campaigning last month in Haifa. “But I believe that we have to talk about our Jewish identity. That’s the main thing that unites us all.”
The remark was a dog whistle for the right-of-center voters that Mr. Gabbay hopes to peel away from Mr. Netanyahu, said Yehuda Ben-Meir, a veteran of right-wing governments who now tracks public opinion for the Institute for National Security Studies in Tel Aviv.
“The left went crazy,” Mr. Ben-Meir said, “but the right paid attention.”
Mr. Gabbay seems pleased by the attention he is getting, critical or not, though he welcomes it nonchalantly, as if it were a matter of simple math.
Indeed, there is a directness to him, from the coolheaded way he fields questions from voters — listening to them all, to gauge the room, before patiently answering each — to how he decided to run in the first place.
His unlikely path began in the executive suite at Bezeq, Israel’s state-owned telecommunications company, where his father had been a technician. Named its chief executive in 2007, Mr. Gabbay led the company through six years of deregulation, privatization and profit, firing a whole layer of managers so gently, according to one account, that they left his office smiling.
After trying to buy El Al, the national airline, Mr. Gabbay, by now a multimillionaire, helped found the center-right Kulanu party in 2015 and then, when it joined Mr. Netanyahu’s coalition, became environmental minister.
He had some successes, but he got no help from Mr. Netanyahu in cutting regulation, he complained, and was the lone vote in the cabinet against a big natural gas deal, which he said would cost consumers far too much.
All the while, he said, he watched Mr. Netanyahu sowing division and hatred at his Sunday cabinet meetings. “Every week it’s like something against somebody,” Mr. Gabbay said in an interview. “It’s against the left, it’s against the media, against Arabs, and against, against, against.”
His final straw was Mr. Netanyahu’s appointment of Avigdor Lieberman, a hard-line nationalist with few relevant qualifications, as defense minister.
“You have to know something about” defense, Mr. Gabbay said, adding: “It’s not like being a minister of environmental protection.”
So in May 2016, Mr. Gabbay quit.
After retreating to Mykonos in Greece, toting biographies of the former prime ministers David Ben-Gurion and Menachem Begin, Mr. Gabbay said he decided to run for prime minister himself to change the political culture in Israel, something that he says can only be achieved from the very top.
He chose Labor as his vehicle like a motorhead snapping up a wreck to restore: Its poll ratings were at record lows, and it was projected to win only eight of 120 Knesset seats. “People told me, ‘You are crazy,’” he said. “‘You are going to join this corpse? Seriously?’”
They may not have appreciated his endurance. A veteran of eight marathons, with a tattoo of a runner under his suit, he barely caught his breath after the primary before beginning his campaign for prime minister, even though an election could be a year or two away.
To Mr. Gabbay, the biggest problem with Mr. Netanyahu, and what will make it difficult to topple him, is his exploitation of identity politics, all too easy in Israel’s fractured society. “The mission of a prime minister is to be a prime minister of all the people in the country — not your camp, your side,” he said.
That said, Mr. Gabbay, a son of Moroccan immigrants who spent his early years in a transit camp, can hope for support from other Mizrahi Jews, whose resentments have been a powerful force in the past. “I am coming from the people, I am not from the elite,” he said. His wife is a teacher; a brother drives a taxi. He would doubtless be the first prime minister who once waited tables in the Knesset cafeteria.
A self-declared social democrat, he assails dog-eat-dog capitalism and pledges to repair the safety net and solve the country’s critical shortage of affordable housing. “We have to change Israel from a country where people just survive,” he said, “to one where people actually live.”
He promises to tackle corruption, and wants to give preferential treatment to military veterans, and not press ultrareligious men into service. “I am coming from a position of ‘in favor of,’ not ‘against,’” he said, comparing himself with rivals who “are against the Arabs and Haredim. I am in favor of my kids.”
The distinction, he added, was not lost on the Orthodox: “They like it very much.”
While he supports a two-state solution for the Israeli-Palestinian conflict, Mr. Gabbay refuses to say what he’d give up for peace, only discussing what he wants to get — a demurral that is likely to be tested in the coming week in meetings in the United States, including a high-profile turn at the Saban Forum in Washington.
Many Israelis find it hard to distinguish between Mr. Gabbay’s positions and those of Mr. Lapid, a former television host and minister who is again second to Mr. Netanyahu in more recent polls. Dahlia Scheindlin, a pollster for Labor in 2015, said politicians with greater skills than Mr. Gabbay had tried that before, but found too few center-right voters to chase. Labor, so identified with the left, she said, “practically doesn’t exist in their eyes.”
But between them, Mr. Gabbay and Mr. Lapid could possibly steal enough support from the right to deny it an automatic majority. And Mr. Gabbay, while insisting he would win, also concedes he would be willing to serve under Mr. Lapid.
For younger Laborites, who barely remember the party’s most recent victory, in 1999, the excitement surrounding Labor is intoxicating.
“He’s not like the old left wing,” said Oren Idel, 23, a student at the Technion university in Haifa. “He’s a new Labor. I think he will bring a lot of voters back to us. He gives me a strong feeling that he’s someone we can trust.”