The meeting between Mr. Netanyahu and the publisher of Yediot Aharonot, Arnon Mozes, took place in 2014, according to Channel 2, but the discussion does not appear to have materialized into action.
Still, the disclosure caused an uproar. Critics accused Mr. Netanyahu and Mr. Mozes of plotting to upend the democratic principle of an independent, free and professional press.
“We expect in a democratic country that the journalistic coverage will come from the editorial echelon, from the reporters, the editors — people who are driven by the public good and the supply of information,” Prof. Rafi Mann, an expert in Israeli media history and communications at Ariel University in the West Bank, told Israel Radio.
It would be improper, he said, for Yediot Aharonot to change its coverage not for the sake of balance or accuracy, but “because the owner wants to save the paper or make things easier financially.”
Yediot Aharonot has struggled financially in recent years, largely because of competition from Israel Hayom, a free daily backed financially by one of Mr. Netanyahu’s main patrons, the American billionaire and Republican Party donor Sheldon Adelson. Since Israel Hayom began publishing in 2007, it has cut deeply into Yediot Aharonot’s advertising base and readership.
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.
There was no immediate response to the reports on Sunday from Mr. Mozes.
Ron Yaron, the editor in chief of Yediot Aharonot, wrote in a letter to the newspaper’s staff that the editors and reporters had been unaware of the meeting between the publisher and the prime minister.
“Naturally, since we knew nothing about it, we also could not ‘act accordingly,’” Mr. Yaron wrote. “Everything published in Yediot Aharonot stands up to the rules of journalism and stems from professional considerations.”
Liron Vardi Geler, a spokeswoman for Israel Hayom, declined to comment.
Yediot Aharonot was once Israel’s most widely circulated newspaper, but industry figures for the first half of 2016 show that Israel Hayom now circulates more copies on weekdays than any Israeli paper.
Legal and political experts debated on Sunday whether the discussion between Mr. Netanyahu and Mr. Mozes constituted criminal behavior or just represented questionable conduct.
Dan Margalit, a veteran Israeli journalist and a columnist at Israel Hayom, told Channel 2: “Let the bosses fight it out. I’m glad I am not involved.”