Mr Brown had told the Leveson Inquiry the Tories agreed to cut funding for the BBC and media regulator Ofcom in return for political support from NI.
But Mr Cameron said the suggestion was “complete nonsense”.
He said he had “never traded a policy” in return for media backing.
Mr Cameron is a friend of ex-News International boss Rebekah Brooks, and hired ex-News of the World editor Andy Coulson as his communications chief.
But Mr Cameron said there had been “no overt deals”, “no covert deals” and “no nods and winks” with the company.
He said he did have some conversations with editors in which he told them “we’d love a bit more support from your paper”, but “not very often”.
Policies relating to Ofcom and the BBC were “born out of proper Conservative thinking about the media”, he insisted, not any kind of deal.
Newspaper reporting and coverage feels like you’re being shouted at rather than spoken to”
David CameronPrime Minister
The prime minister’s witness statement reveals he had 1,404 meetings with “media figures” – 26 a month on average – while in opposition between 2005 and 2010. Once in government, that fell to an average of about 13 a month.
“Most of these meetings were about me trying to promote Conservative policy,” he said.
In 2008 he took a trip to the Greek island of Santorini for a dinner with News International boss Rupert Murdoch because it was a chance to “build a relationship” with him.
A text message sent by Mrs Brooks to Mr Cameron in October 2009 was read to the inquiry in which she said she was “rooting for him”, both as “a personal friend” and because “professionally we’re in this together”.
The PM said that was a reflection of the fact that the Sun had the previous week switched its support to the Conservatives.
Mrs Brooks and her husband Charlie – who went to school with Mr Cameron – have both been charged with conspiracy to pervert the course of justice in relation to the phone-hacking scandal surrounding News of the World. Both deny wrongdoing.
Earlier Mr Cameron said politicians “have to take care when you have personal friendships [with individuals in the media] but that can be done and I have done that”.
The prime minister was also asked about his decision to employ Mr Coulson after he had resigned from the News of the World.
He said he accepted it was “a controversial appointment” which had “come back to haunt him and me”, but he had been given “assurances” at the time by Mr Coulson that he had no knowledge of phone hacking.
“I sought assurances, I got them and that was the basis on which I employed him,” the PM added.
Mr Cameron’s appearance at the Royal Courts of Justice in London is part of the inquiry’s examination of the relationship between politicians and the media.
He said that relationship had deteriorated, meaning “a lot of politicians think the press always get it wrong” and the press think politicians “are just out for themselves”.
“It’s become a bad relationship. How we get it to a better place, I think part of it will be about transparency, better regulation, having a bit more distance, that will be part of respect.
“But respect has to come from high standards in both places… respect has to be earned on both sides.”
He continued: “When I say distance, partly what I mean is that the politicians… have got to get out of the 24-hour news cycle, not try and fight every hourly battle, focus on long-term issues and be prepared to take a hit on a story they don’t immediately respond to.”
Mr Cameron said the rolling, 24-hour news agenda meant newspapers had been forced to “turn up the volume” on their coverage, and focus on “finding an angle” rather than reporting facts alone.
“I think that newspaper reporting and coverage feels like you’re being shouted at rather than spoken to.”
He said the inquiry was a “cathartic moment” and a chance to “reset” relations.
The Conservatives have been accused of having a biased view in favour of the bid by News International’s parent company News Corp to take over BSkyB.
The inquiry is likely to ask Mr Cameron about Culture Secretary Jeremy Hunt’s handling of the BSkyB bid, which was abandoned in July 2011 amid outrage over the phone-hacking scandal.
The inquiry previously heard that Mr Hunt sent a memo to Mr Cameron voicing support for the bid before he was put in charge of overseeing it at the end of 2010.
Labour accuse Mr Hunt of being too close to News Corp, but the prime minister has backed Mr Hunt amid calls for him to resign.
Shortly after the prime minister arrived at the Royal Courts of Justice, the Metropolitan Police announced that three people, including a former prison officer, had been arrested as part of a probe into alleged corrupt payments to public officials.
The Crown Prosecution Service has also announced that Guardian journalist David Leigh, who admitted hacking an arms company executive’s phone, will not face charges.