The seeming dissonance between a rise in the polls and the prime minister’s deepening legal troubles makes complete sense to Mr. Netanyahu’s defiant base in Kiryat Malachi and in other strongholds of his conservative Likud party. In these parts, Bibi, as he is lovingly nicknamed, is extolled as a popular hero who is persecuted by a liberal news media; a leader without peer whose peccadilloes are easily forgiven.

Mr. Netanyahu, Israel’s longest serving prime minister after the country’s founder, David Ben-Gurion, has been mired for months in corruption investigations involving allegations of some $300,000 worth of illicit gifts, including expensive cigars, jewelry and champagne, and back-room dealings to ensure more favorable media coverage. Last month, police recommended that he be charged with bribery, fraud and breach of trust in two separate cases. He has since become a suspect in a third, weightier scandal involving an Israeli telecommunications and media tycoon.

Another former prime minister accused of graft did not fare as well. Ehud Olmert, who originally came from Mr. Netanyahu’s Likud party, was forced out of office under public and political pressure in 2008. Conversely in Mr. Netanyahu’s case, the more sensational the leaks from the investigations, the more popular he seems to grow.

Though a recent coalition crisis was resolved and elections are not scheduled until late 2019, a steady stream of newspaper and television polls have put Likud in front. Those polled consistently chose Mr. Netanyahu as the most suitable candidate, by far, for prime minister.