Downing Street rejected calls for Culture Secretary John Whittingdale to step aside from decisions about press regulation after he disclosed that he had a relationship with a sex worker.
A senior Downing Street spokesman said: "The Prime Minister has got full confidence in John Whittingdale to carry out all of his duties."
The spokesman confirmed that Whittingdale did not inform the Prime Minister about press interest in his relationship when he was appointed to the Cabinet after the 2015 General Election.
The Prime Minister learnt about the affair about 10 days ago when the story emerged on the internet, the spokesman said, adding it was a decision for Whittingdale whether he felt it necessary to inform him.
Although the relationship took place before he was made a minister, Whittingdale was at the time chairman of the influential Commons Culture, Media and Sport Committee which had held a series of high-profile hearings on the phone-hacking scandal.
BBC2's Newsnight reported that four newspapers - The People, The Mail on Sunday, The Sun and The Independent - had investigated the claims at the time but concluded it was not a public interest story.
Members of the Hacked Off campaign said the Culture Secretary had been "compromised".
But the executive director of the Society of Editors, Bob Satchwell, said it is a "preposterous conspiracy theory too far" to say newspapers and broadcasters "jointly decided not to publish" the story.
The Number 10 source declined to say whether Mr Cameron believed the media should have published the story, saying only that this was a decision for newspaper and broadcast editors.
"The British press, as we have seen in recent days, are very vigorous in their pursuit of stories," said the source. "He is not going to pass judgment on things like that."