Lord Justice Leveson has vowed not to be pushed off course by attempts to portray questions about the conduct of the press as an attack on free speech.

The judge, who is leading the inquiry into media standards, insisted he had no "hidden agenda" to stifle reporting as he explained why he raised concerns with Downing Street that his investigation could be undermined.

He spoke out in response to a newspaper report that he threatened to quit over remarks by cabinet minister Michael Gove that the probe was having a "chilling effect" on journalism.

In a 20-minute statement at the opening of proceedings, he did not address directly whether or not he had put his position on the line over the issue or sought to "gag" the Education Secretary.

But he confirmed that he contacted Cabinet Secretary Sir Jeremy Heywood to discuss whether the remark - and its apparent backing by David Cameron - represented a "settled view" within the Government against regulation.

He said such a development "would clearly have raised questions about the value of the work that the inquiry was undertaking at substantial cost.

"Put shortly, I was concerned about the perception that the inquiry was being undermined while it was taking place."

The inquiry chair, who said he accepted Sir Jeremy's reassurances that that was not the case, added that he had no argument with the Mail on Sunday's right to publish its original story - or with other newspapers printing versions of it.

He said: "It is absolutely correct that the press should be able to hold this inquiry in general and me in particular to account."

But, he added: "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 of reference that have been set for me."