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Mr. Bennett turned to politics after the sale of Cyota and served as Mr. Netanyahu’s chief of staff for two years. They parted ways after a mysterious falling out that he won’t discuss but that Israeli media have linked to Mr. Netanyahu’s wife, Sara, who wields great influence over the prime minister’s inner circle.

He and Mr. Netanyahu clashed again when Mr. Bennett, then leader of the mainstream settler group, fiercely opposed MR. Netanyahu’s decision in late 2009 to slow settlement construction for 10 months in a U.S.-led effort to encourage Palestinians to renew peace talks.

This year, he took his positions to the national political arena. Two months ago, he captured the chairmanship of the stodgy Jewish Home party from its colorless leader and set out to transform the party’s image. Mr. Bennett took his campaign everywhere from remote West Bank settlement outposts to trendy bars in Tel Aviv.

The strategy worked, and Jewish Home started gaining in the polls.

Evidence that Mr. Bennett was a political force to be reckoned with came this week when Israel‘s top-rated comedy show, “A Wonderful Country,” introduced a new character, iBennett: a user-friendly app that shows a broadly smiling Bennett look-alike making extremist political pronouncements — described as bugs in the system.

Mr. Netanyahu hit back after Mr. Bennett told a TV interviewer last week that he would personally prefer to go to jail than to obey an order to evict Jewish settlers from their homes under a peace deal, as happened when Israel withdrew from the Gaza Strip in 2005.

The prime minister summoned all three major Israeli TV stations for rare domestic interviews and announced that anyone who preached insubordination in the military would not be welcome in his next government. Mr. Netanyahu’s camp then followed up with a campaign of posters and newspaper ads depicting Mr. Bennett as irresponsible and extremist.

Mr. Bennett says that his comments have been distorted, that he wasn’t preaching insubordination but voicing his own personal opinion — one that resonates widely within the religious right, which was traumatized by the Gaza pullout.

“I think people are looking for the truth and are drawn to real people who speak at eye level, even if sometimes they make mistakes,” he said. “It was an unfortunate comment, but aside from wars, I don’t think the prime minister ever calls all the TV stations to him at once. The public isn’t buying this spin and rejects it entirely.”

Despite the campaign conflicts, Mr. Bennett insists he can work with Mr. Netanyahu.

“The question is who will be by his side,” he said. “Netanyahu will drive the bus, but I refuse that he be alone at the wheel. I’ll be there to put a hand on the wheel and influence where it goes.”