Leveson reveals inquiry concerns
Lord Justice Leveson said he contacted Number 10 because he was concerned about "the perception" his inquiry into press standards was "being undermined".
The judge said he had asked the cabinet secretary if the government had already reached a "settled view" on future regulation, but was assured it had not.
His phone call came after Michael Gove said he feared the inquiry was having a "chilling atmosphere" on free speech.
The judge told his inquiry he had no "hidden agenda" to stifle a free press.
Lord Justice Leveson's statement followed claims published by the Mail on Sunday (MoS) that he had threatened to quit.
The newspaper said he made his threat following comments by Mr Gove to a press gallery lunch in February that there was "a chilling atmosphere towards freedom of expression which emanates from the debate around Leveson".
MoS political editor Simon Walters, co-author of the article, later gave evidence but the judge said he had no intention of asking about the resignation story, and had called him to appear before the article was written.
Earlier, the judge confirmed he had contacted Cabinet Secretary Sir Jeremy Heywood about Mr Gove's comments, and Mr Cameron's subsequent statement at Prime Minister's Questions that his education secretary was "making an important point".
The judge told the inquiry he had felt it "necessary and appropriate" to raise the issue with Sir Jeremy.
"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."
He said Sir Jeremy assured him 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 told the inquiry he considered convening a special session to deal with the MoS article, but decided against it on grounds of cost.
He said 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.
He said he had given "core participants" to the inquiry 48 hours to make any submissions or observations concerning the report but that, despite the "very serious allegations" in the report, the paper's publisher, Associated Newspapers, had not responded.
The judge said the MoS had been entitled to publish its story, and went on: "I will not be deterred from seeking to fulfil the terms the reference that have been set for me."
Andrew Grice, the political editor of the Independent, Peter Riddell, former chief political commentator for the Times, and Philip Webster, former political editor of the Times and current editor of thetimes.co.uk, also gave evidence.
'Asking for trouble'
They were asked about the relationship between the press and politicians.
Mr Walters told the inquiry it was an "open secret" that Downing Street, under the previous Labour government, could pick up the phone and "dictate an article in certain News International journals".
Mr Grice earlier said he suspected there was a "you scratch my back and I'll scratch yours" understanding that developed between Labour and News International.
Mr Riddell said the only time he met James Murdoch was at a "pretty gruesome" dinner hosted by Alistair Darling, then Chancellor of the Exchequer. Mr Murdoch criticised Mr Darling over dinner for an earlier decision on BSkyB and ITV. "It was all just a bit embarrassing," said Mr Riddell.
Mr Webster described the treatment of some politicians, including John Major, Neil Kinnock and Gordon Brown, at the hands of the press as too personal at times.
Channel 4 news anchor Jon Snow later told the inquiry he suspected the relationship between the press and politicians was too close, but "we didn't ask questions about it".