JERUSALEM — Prime Minister Benjamin Netanyahu of Israel was questioned by the police on Friday as a possible suspect in a third bribery case, the weightiest so far in a string of corruption investigations that are jeopardizing his political future.

Officers questioned Mr. Netanyahu about a case involving Shaul Elovitch, an Israeli telecommunications tycoon accused of using his popular Hebrew news site to provide positive coverage of Mr. Netanyahu and his wife in return for regulatory and financial benefits worth tens of millions of dollars.

A large black screen was drawn on Friday morning across leafy Balfour Street in Jerusalem, concealing the prime minister’s official residence and the comings and goings of investigators. Outside, a small but noisy group of demonstrators beat drums and held placards with slogans against corruption.

Mr. Netanyahu, who has now been questioned by the police eight times in the past 14 months, is fighting for his political life as the allegations against him mount. Last month, the police recommended that Mr. Netanyahu be charged with bribery, fraud and breach of trust in two other graft cases involving allegations of illicit gifts for favors and another attempt to obtain more favorable coverage.