TEL AVIV—Israeli Prime Minister Benjamin Netanyahu is betting his political survival on a dedicated base of conservative voters that he hopes will ignore potential bribery charges that could undo his bid for a fifth term.

All but one of his current coalition partners threw their support behind Mr. Netanyahu after Israeli Attorney General Avichai Mandelblit’s decision Thursday to charge the prime minister with bribery, fraud and breach of trust, pending a hearing. The allegations include charges that Mr. Netanyahu tried to...