The culture secretary, Jeremy Hunt, has been accused of acting as a "cheerleader" and operating a secret back channel with News Corporation executives to assist the passage of the company's bid for full control of BSkyB.

The charges against the cabinet minister emerged during questioning at the Leveson inquiry on Tuesday over a series of emails submitted to the inquiry by Rupert Murdoch, News Corp chairman and chief executive.

His son, James, was shown some of the emails written by his chief lobbyist, Frédéric Michel, which appeared to show that News Corp was in close communication with Hunt when the business secretary, Vince Cable, was deciding on the bid to take over the pay-TV giant BSkyB.

Hunt's special adviser phoned Michel on 15 June 2010, shortly after the £8bn takeover was announced, to tell him in an email he sent to Murdoch that there "shouldn't be media plurality issue [with News Corp's bid for Sky] and believed the UK government would be supportive throughout the process".

The culture secretary then phoned Michel directly, according to Michel's email, on 15 July 2011 to say that he had just given an interview to the Financial Times. Ahead of publication, Hunt told Michel – according to the News Corp's lobbyist's email – that he had told the newspaper that "he didn't see any problems" with the News Corp bid for Sky.

Counsel for the inquiry Robert Jay, QC, suggested to Murdoch it was "clear that you were receiving information along the lines that the UK government as a whole would be supportive of News Corp".

Murdoch responded that Hunt had said as much publicly and that it was "not necessarily inappropriate" that "the DCMS part of the government [was] saying we don't see any issues here ... it is going to be fine".

Hunt was handed a quasi-judicial responsibility for the bid as culture secretary in December 2010 after responsibility for media ownership was taken away from Cable.

The hearing also heard that James Murdoch discussed the BSkyB bid with David Cameron briefly at a meal at then News International chief executive Rebekah Brooks's house on 23 December 2010. Cameron later told parliament he held no "inappropriate" conversations with Murdoch. Murdoch also revealed he spoke about the BSkyB bid with the chancellor, George Osborne, at a time when he was feeling "grumpy" over media regulator Ofcom's referral of the deal.

Jay also referred to a blog written by the BBC business editor, Robert Peston, stating that Ofcom was expected to review News Corp's bid for Sky, and that Michel was able to contact Hunt and report, "Jeremy Hunt is not aware and thinks it is not credible at all, and he is checking now". Leveson said the evidence showed that Michel was able to check the veracity of the Peston blog with Hunt's office within seven minutes.

Murdoch said: "At this time I was repeatedly seeking official meeting with Mr Cable and we were not able to have this meeting." He denied that News Corp had instead chosen to communicate through Hunt, whom Jay described as a "cheerleader" for the company.

Murdoch replied that he thought this description of Hunt was "unfair".

Jay said the Michel phone calls and emails being discussed were generally between the News Corp lobbyist and Hunt's special adviser, Adam Smith, rather than the culture secretary himself. However, Hunt is likely to face strong criticism of his handling of the BSkyB bid. He will have to explain whether he was aware of his advisers' contacts with News Corps.

Hunt has repeatedly reassured parliament that he handled the bid in a way that was "completely fair, impartial and above board".

In March 2011, Hunt told parliament he had decided not to refer the bid to the Competition Commission as a result of undertakings given to him by News Corp to spin off Sky News as an independent public limited company. In January Ofcom, the media regulator, had recommended the merger be referred to the Competition Commission.

He has also insisted in March that "his department has published all the documents relating to all the meetings, all the consultation documents, all the submissions and we received, all the exchanges between my department and News Corporation".

The Labour party is likely to demand an urgent Commons statement from Hunt to set out the nature of his exchanges with News Corp both before and after he was given quasi-judicial responsibility for the takeover.

The private exchanges suggest that Hunt and his special advisers, notably Adam Smith, his chief of staff, were active advocates for the takeover within Whitehall before being handed direct ministerial responsibility for the issue.

The cabinet secretary, Lord O'Donnell, had rejected complaints that Hunt was not capable of making an impartial ruling on the takeover.

Hunt has repeatedly assured MPs that he was acting in a fair and transparent way.

When the hearing at the Royal Courts of Justice resumed after lunch on Tuesday, Jay, said the Michel emails showed informal contact took place "secretly" between the News Corp lobbyist and Hunt's special adviser. Murdoch said this was "acceptable and part of the process".

The counsel for the inquiry then said further emails would raise the question whether the contacts "fell into the appropriate box or the inappropriate box".

On 23 January 2011, after he had taken over responsibility from Cable for the Sky deal, Hunt believed it was "almost game over" for those who opposed News Corp's takeover of BSkyB, according to the contents of a Michel email read out by Jay.

In another Michel email following discussions with Hunt's special adviser, Murdoch is given information about timetables and Hunt's view of the merits of News Corp's case, Jay said.

"His view is that once he announces publicly he has a strong UIL [undertaking in lieu] it's almost game over for the opposition," Jay added, reading from the email.

This email was sent shortly before Hunt updated parliament on the Sky takeover deal.

Jay, quoting again from the Michel emails, told the inquiry that earlier in the regulatory process Hunt was "very frustrated" that he received "strong legal advice" not to meet with Murdoch about the Sky bid. Murdoch said he was "displeased" with this.

According to Jay, Michel then advised Murdoch to "have a chat with him [Hunt] on his mobile, which is fine".

When asked if he thought this a surreptitious phone call , Murdoch replied "not to my mind". Hunt later called Murdoch to apologise for a cancelled meeting, he added.

Jay read another email from Murdoch to Michel in which the former said "you must be fucking joking. I will text him and find a time" to meet . Murdoch responded: "As I said earlier, I was displeased."

After Ofcom raised issues with the Sky bid, on 14 December 2010 Michel emailed Murdoch saying he had a "very good debrief with Hunt ... he is pretty amazed by its findings, methodology and clear bias. He very much shares our views on it." Michel said he would try to set up a meeting with Hunt before Christmas.

Jay asked whether Murdoch took Hunt references to mean him personally or his office. "Communicating through his office ... I didn't assume it was all direct," replied Murdoch.

"But I think you can appreciate the channel wasn't of my primary concern, it was the content of the notes which were confirming our concerns about the process."

The Leveson inquiry was told that there are 163 pages of Michel emails, and it is likely that the younger son of Rupert Murdoch – who was personally charged with seeing the BSkyB bid through – will be shown more emails written to him by the company's UK lobbyist in chief.

Michel is a close ally of James Murdoch at News Corp, part of a small team of trusted executives, whose job was to get close to politicians and lobby on behalf of the company. Murdoch said he was a "diligent public affairs executive".