Lord Justice Leveson said today that he had no "hidden agenda" to stifle press freedom.
The judge, who is heading the inquiry into media standards, insisted he would not be deterred from fulfilling his terms of reference following reports suggesting he was ready to resign after Education Secretary Michael Gove said his inquiry was having a "chilling" effect.
He acknowledged there were concerns within the media about the impact of the inquiry, but insisted that he was fully committed to press freedom.
"I also understand that, on every day of the inquiry, every exchange I have with a witness will be analysed in order to reveal a hidden agenda. There is none," he said.
"No recommendations have been formulated or written. No conclusions have yet been reached."
Lord Justice Leveson confirmed he had contacted the Cabinet Secretary, Sir Jeremy Heywood, after Mr Gove made his remarks to a Parliamentary Press Gallery lunch last February and David Cameron subsequently appeared to back them up at Prime Minister's Questions.
"From my perspective, the issue was straightforward. Had the Government reached a settled view along the lines that Mr Gove had identified, it would clearly have raised questions about the value of the work that the inquiry was undertaking at substantial cost," he said.
"I recognised that the Prime Minister had said that it was right to set up the inquiry but I wanted to find out whether Mr Gove was speaking for the Government, whether it was thought that the very existence of the inquiry was having a chilling effect on healthy, vibrant journalism, and whether the Government had effectively a settled view on any potential recommendations.
"Put shortly, I was concerned about the perception that the inquiry was being undermined while it was taking place."
Following Mr Cameron's appearance at Prime Minister's Questions, the judge said he had felt it "necessary and appropriate" to raise the issue with Sir Jeremy.
"I received the assurance that no fixed view had been formed and it was wrong to infer from the Prime Minister's observations any concerns or collective view."
Lord Justice Leveson said The Mail on Sunday, which earlier this month carried an account of his conversation with Sir Jeremy, had been entitled to publish its story "with whatever comment they considered appropriate".
"It is absolutely correct that the Press should be able to hold this inquiry in general and me in particular to account," he said.
"Having said that, however, it is at least arguable that what has happened is an example of an approach which seeks to convert any attempt to question the conduct of the Press as an attack on free speech.
"For my part, I will not be deterred from seeking to fulfil the terms the reference that have been set for me."Suggest a correction