Mr. Netanyahu has a combative relationship with much of the Israeli news media.

In a Facebook post in 2015, Mr. Netanyahu accused Mr. Mozes of “an orchestrated and ridiculous campaign of slander” against him, his Likud Party and Israel Hayom. The attack came a day after lawyers filed a petition to ban Israel Hayom during that year’s election campaign, calling it a “propaganda platform” that is “masquerading as a newspaper.”

The election was called after Mr. Netanyahu broke up his government coalition, partly to prevent the advancement of a bill to outlaw free newspapers like Israel Hayom.

The meeting between Mr. Netanyahu and Mr. Mozes in 2014 was recorded at Mr. Netanyahu’s request by his former chief of staff, Ari Harow, according to Channel 2. It surfaced during a separate police investigation of Mr. Harow on suspicion of financial irregularities.

Fraud investigators questioned Mr. Netanyahu twice last week, with the police saying that he was asked about two cases. One, a possible graft case, involves the receipt of gifts from business executives, apparently including regular deliveries of expensive cigars and pink champagne from a Hollywood producer and longtime friend, Arnon Milchan.

Mr. Netanyahu’s lawyer, Jacob Weinroth, said there was “no speck” of criminality in receiving cigars as a present from a friend.

The police provided no details about the second case, saying only that a second suspect had been questioned — presumably Mr. Mozes.

Mr. Netanyahu told a meeting of his Likud Party ministers on Sunday that while he could not go into details, “I know what this is about and I am telling you in full confidence: This will come to nothing because there is nothing.” He has made a mantra of the phrase in recent weeks as he has denied any wrongdoing.