On Thursday evening, for the second time this week, investigators grilled Prime Minister Benjamin Netanyahu of Israel at his official residence as a suspect in an investigation into possible corruption, the details of which have largely been kept under wraps.

The police said in a brief statement that Thursday’s session had lasted five hours and that Mr. Netanyahu had been questioned under caution on suspicion of receiving improper gifts and favors. He was also interviewed about a separate case, the police said, without offering any details.

Even as the questioning was underway, Israel’s news media were reporting about some gifts that had led to suspicions of graft.

A Hollywood producer and longtime friend of Mr. Netanyahu’s is said to have supplied him with boxes of cigars for years, the Haaretz newspaper and Israel’s Channel 2 News reported. The news channel added that the American-Israeli producer, Arnon Milchan, had brought Mr. Netanyahu’s wife, Sara, bottles of fine Champagne.

Jayna Zelman, a spokeswoman for Mr. Milchan, an Israeli intelligence operative decades ago and a producer of “Gone Girl,” “12 Years a Slave” and many other films, declined to comment.

Israel’s attorney general, Avichai Mandelblit, outlined the investigation after the first session of questioning on Monday night, saying it involved gifts and benefits that the prime minister had received from business executives. Investigators have gathered testimony from dozens of witnesses, Mr. Mandelblit added, some of them abroad.

Mr. Netanyahu has vehemently denied any wrongdoing, repeating the mantra that the investigation will amount to “nothing, because there is nothing,” and accusing the news media and opponents of hounding him. A political survivor who is serving his third consecutive term as prime minister and his fourth over all, he and his wife have come under scrutiny for years for what critics describe as a taste for the high life at the expense of others.