Lord Justice Leveson today insisted he had no 'hidden agenda'to undermine press freedom.
Leveson was responding to a Mail on Sunday story last week claiming he had threatened to quit after education secretary Michael Gove said the inquiry was a having a 'chilling effect'on free speech.
In an address to the inquiry this morning, Leveson confirmed he did raise concerns with cabinet secretary Jeremy Haywood and he did not deny claims he had threatened to resign.
Leveson insisted he had 'consistently and repeatedly emphasised the critical significance of free speech'during the inquiry, adding: 'It's absolutely correct that the press should be able to hold this inquiry in general and me in part to account."
Leveson said the Mail on Sunday, and other papers that followed up the story, were 'entitled to do so with whatever comment they considered appropriate…
'Having sad that, however, it is at least arguable that what has happened is an example of an approach that seeks to convert any attempt to question the conduct of the press as an attack on free speech,'he added.
'For my part I will not be deterred from seeking to fulfil the terms of reference that have been set for me."
He continued: 'I understand only too well the natural anxieties of editors, journalist and others of dangers of a knee-jerk response to the events of last July.
'While I continue to state my belief in a free press at every possible opportunity, and not a single witness has sought to suggest that healthy and vibrant journalism is not essentially to our society, I also understand that on every day of the inquiry, every exchange that I have with a witness will be analysed and considered in order to reveal the hidden agenda. There is none.
'No recommendations have been formulated or written, no conclusions have yet been reached. Testing propositions is not any equivalent to the expression of views concluded."
He said Gove had gone 'further than emphasising the importance of freedom of expression'by speaking of the 'dangers that the cure is worse than the original disease'during his speech to political journalists at a House of Commons Press Gallery lunch on 21 February.
As Gove occupied a senior position in the Cabinet, Leveson questioned whether he was speaking for the Government.
His fears were underlined the following day when David Cameron said at Prime Minister's Questions that Gove was making an 'important point".
Leveson said it seemed to him that Cameron's response was 'open to the suggestion that he was indeed agreeing with Mr Gove's views".
He said: '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 the inquiry was undertaking at substantial cost."
Leveson was also 'concerned about the perception that the inquiry was being undermined while taking place".
He 'considered it necessary and appropriate'to make inquiries of cabinet secretary Jeremy Haywood, when he received assurance that 'no fixed view had been formed'by the Government.
'I fully accepted that assurance,'said Leveson.
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