Israeli media have reported the existence of an audiotape that is increasing pressure on Prime Minister Benjamin Netanyahu, who is facing an inquiry into corruption allegations.
The tape purports to carry a conversation with a newspaper owner in which they discuss actions that would be mutually beneficial.
Mr Netanyahu was questioned by police last week in two different cases.
On Sunday he repeated that "nothing's going to come" out of the inquiry.
The details of the conversation on the audiotape were carried in a report on Channel 2 television and the Haaretz newspaper.
They claim that the second person on the tape is Arnon "Noni" Mozes, the publisher of the Yedioth Ahronot newspaper.
Channel 2 and Haaretz allege that on the tape Mr Netanyahu offers Mr Mozes a deal under which the circulation of the competitor daily Israel Hayom would be limited in return for more favourable coverage of the PM in Yedioth Ahronot.
It was unclear when the purported conversation took place, although Haaretz said it may have been several months ago.
Haaretz said that Mr Mozes had also been questioned last week.
Israeli media have covered the story widely and say there has been no response so far from Mr Netanyahu or Mr Mozes.
Mr Netanyahu did speak on Sunday, before the Channel 2 report aired.
The Jerusalem Post reported him as telling his Likud party ministers: "To my dismay I cannot provide details. What I can tell you today, now that I know what this is about, and I will tell you this with full confidence: nothing will be found because there is nothing.
"What we do have here is wrong, incessant pressure that media elements are applying on law-enforcement officials. They're blowing balloons and hot air is coming out of them, one by one. It will be the same in this case."
Mr Netanyahu, 67, was twice questioned last week, on matters referred to as Case 1000 and Case 2000.
Case 1000 is said to concern the alleged acceptance of "improper gifts" worth thousands of dollars from businessmen.
There have been no official details at all on Case 2000.
Opponents of Mr Netanyahu had called for an investigation into his affairs following a series of scandals in recent months - none of which has resulted in charges.
Tzipi Livni, of the Zionist Union, said on Saturday that Mr Netanyahu had "lost the moral authority to be prime minister" and "must decide if he wants to be an oligarch or a prime minister", the Jerusalem Post reported.