James Murdoch met David Cameron 12 times while he was leader of the opposition, including four meetings also attended by Rebekah Brooks, the Leveson Inquiry heard on Tuesday.
The media mogul also briefly talked to Cameron at a dinner about the removal of Business Secretary Vince Cable's powers to oversee News Corporation's bid to take over broadcaster BSkyB after the coalition had come to power.
Murdoch had drinks with the Tory leader in September 2009 to discuss The Sun's plans to endorse the Conservative Party at the following year's general election, the press standards inquiry was told.
He also met George Osborne and William Hague during the Tories' time in opposition.
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Between June 2006 and January 2010, Murdoch met Cameron eight times for dinner, twice for breakfast, once for lunch and once for drinks.
Brooks attended meetings between the media boss and the Conservative leader on 5 May 2009, 2 November 2009, 19 November 2009 and 21 January 2010.
After Mr Cameron entered Number 10 in May 2010, Murdoch and his family had lunch with him at the Prime Minister's country retreat, Chequers in Buckinghamshire, in November 2010.
Brooks and her husband, Charlie, hosted a dinner attended by the media mogul and Cameron on 23 December 2010.
This was two days after Cable was stripped of his responsibilities for regulating the media after he was caught on tape by undercover reporters claiming to have "declared war" on Rupert Murdoch's News Corp empire.
James Murdoch told the Leveson Inquiry that he and Cameron mentioned what had happened.
"He reiterated what he had said publicly, which is that the behaviour had been unacceptable, and I imagine I expressed the hope that things would be dealt with in a way that was appropriate and judicial," he said.
"It was a tiny conversation ahead of a dinner where all these people were there, so it wasn't really a discussion."
The inquiry heard that Mr Murdoch had lunch at Chequers with Tony Blair when he was prime minister in July 2004.
He also held a conference call with Mr Blair in October 2005 during which he may have discussed European Commission proposals for regulating broadcasting rights for English Premier League football.
James Murdoch (left) met with David Cameron 12 times while the Tory leader was in opposition
Murdoch said: "It was a normal and appropriate or legitimate bit of business advocacy...
"The purpose would be hopefully for senior policy-makers, the prime minister in this case, to understand that some of these policies might have adverse consequences for English football."
Murdoch had two meetings at 10 Downing Street with then-prime minister Gordon Brown in March and December 2008.
He said he could not remember exactly what was discussed, adding: "He would have told me lots of things about the economy and the like."
Murdoch confirmed he was "friendly" with Mr Osborne and had once visited the Chancellor's grace and favour house, Dorneywood in Buckinghamshire, with his family.
He said he had one discussion with Osborne about News Corp's bid to take over BSkyB, which was eventually dropped last July after a public outcry over the revelation that the News of the World hacked murdered schoolgirl Milly Dowler's phone.
Murdoch said his conversation about the proposed buy-out of the satellite broadcaster with the Chancellor "would have just been to be grumpy about it taking a long time and being referred to (regulator) Ofcom, which I was very clear in public about at the same time".
Mr Cameron's official spokesman declined to comment today on Mr Murdoch's account of his meetings with the Prime Minister, and his suggestion that they discussed the BSkyB bid at the December 2010 dinner.
"Everybody expects the Prime Minister to be called (by Leveson), and we have made clear throughout that he will attend and answer the questions that are put," said the spokesman. "But we have always been clear that we should let the inquiry continue and not comment on it as it happens."
Downing Street has previously insisted that the dinner was "a private engagement" and Mr Cameron took no part in the decision-making process on the bid.
The No 10 website records reporters' queries about the dinner last year.
On 14 July, it said: "Asked whether the PM would publish more details about his meeting with Rebekah Brooks and James Murdoch just before Christmas, the PMDS (Prime Minister's deputy spokeswoman) said this was a private engagement and that the PM had responded to a letter from shadow culture secretary Ivan Lewis on this subject and he made clear that he had no role to play in the BSkyB bid."
Then, on 19 July, the website records: "Asked to comment on accusations by John Mann MP that the PM had broken the Ministerial Code by having Christmas dinner with James Murdoch and his wife two days after taking the BSkyB deal from Vince Cable's hands, the PMDS said, quite simply, the PM had not broken the Code.
"She added that he had been clear he had not been part of the process regarding BSkyB and that Jeremy Hunt had taken this on in a quasi-judicial role.
"Asked to consider the fact that the Code states that Ministers must avoid any appearance of conflict, the PMDS said the PM had not been involved in any of the discussions about BSkyB."
Earlier, Murdoch admitted that the News of the World should not have run the Max Mosley "Sick Nazi Orgy" story, which led to the former Formula 1 boss receiving more than £60,000 in compensation.