Responding to the news on Thursday that the PCC's functions would be transferred to "a new press regulator with teeth", Leveson said he had a number of questions about the new set-up and that he was not endorsing it at the present time.
Leveson said he encouraged PCC chairman Lord Hunt to continue pursuing options for the future of press regulation, but he stressed: "It is important that this encouragement should not be taken as endorsement let alone agreement."
He said of Hunt: "He is absolutely correct to observe that from the outset of this inquiry I've said to editors that the problems of press regulation are theirs and they should seek to find a solution.
"The solution must not only work for them but it must also work for me and the public at large."
He added: "To say that the PCC was never a regulator only underlines the concern that the public have been misled about what it could do.
"I do not suggest that Lord Hunt seeks to pre-empt me or that he proceeds on the basis that I have agreed with the approach which he proposes. My mind remains open to all options.
"Lord Hunt and the industry must continue to work on what they see as the best way forward. The ultimate suggestion will be subjected to forensic analysis."
Hunt said last week that the PCC had accepted his proposals to scrap the body "to resume public trust and confidence in the press". He added: "I won't do anything that Lord Leveson doesn't want."
Leveson said today that he had a number of questions about the proposed new set-up, and what would happen to the funding body PressBof and the editors' code committee.
"I must ask whether a five year rolling contract is sufficient to deal with the fundamental problem of industry acceptance," Leveson said.
Leveson also issued a further warning today about material being leaked to the media before it was heard by the inquiry.
He said he would restrict the access conditions for witness statements if leaks continued, and would be asking all the participants with access to confidential information to sign a new agreement.
"It is important to emphasise that early sight of these statements is subject to strict conditions of confidentiality. All those within the core participants and their legal representatives have signed confidentiality undertakings
"Against that background, any leak is very disappointing and a matter of concern. Unless it stops I shall consider restricting the ways in which the statements are made available."
Free daily newsletter
If you like our news and feature articles, you can sign up to receive our free daily (Mon-Fri) email newsletter (mobile friendly).
