Known as “Qatargate,” the case hinges on the claim that Mr. Netanyahu’s media advisers were paid by a representative of Qatar to promote Qatari interests in the Israeli news media. That claim has angered many Israelis because it created the perception of a conflict of interest; for years, Qatar has hosted leaders of Hamas.

Mr. Netanyahu’s recent efforts to fire the head of the Shin Bet, the Israeli internal security agency, has compounded the furor. It was the Shin Bet that first instigated the investigations into Mr. Netanyahu’s aides.