Media playback is unsupported on your device Media caption Jeremy Hunt says he has been "scrupulous" and will not resign

Labour has called for Culture Secretary Jeremy Hunt to resign after Leveson Inquiry evidence appeared to show his support for News Corp's bid for BSkyB.

During evidence from James Murdoch, the inquiry discussed News Corp emails that appeared to show Mr Hunt had privately expressed support .

Labour leader Ed Miliband said Mr Hunt had acted as a "back channel" for the Murdochs and should step down.

But Mr Hunt said he had "conducted this process with scrupulous fairness".

He said he had asked Lord Justice Leveson to bring forward his appearance at the inquiry. Mr Hunt had been due to give evidence along with other politicians, including the prime minister, in May.

"Now is not a time for kneejerk reactions. We've heard one side of the story today but some of the evidence reported meetings and conversations that simply didn't happen," Mr Hunt said in a statement.

In June 2010, News Corp had been bidding to take over the 61% of BSkyB it did not already own. That November, Business Secretary Vince Cable asked media regulator Ofcom to look at the potential impact of the deal on media plurality.

Mr Hunt took over responsibility for overseeing the BSkyB bid after Mr Cable was stripped of the role in December 2010, having been secretly recorded saying he had "declared war" on News Corporation chairman Rupert Murdoch.

Government insiders know that the emails revealed today look and smell bad, but they are hoping that when Jeremy Hunt gets his day in court he will persuade Lord Justice Leveson that they were not improper

The company abandoned the bid in July 2011 after the phone hacking scandal surfaced.

'JH emails'

Mr Murdoch was questioned by counsel for the inquiry Robert Jay QC about his contact with politicians before and during News Corp's bid for BSkyB.

The inquiry considered emails by Frederic Michel, head of public affairs at News Corp.

A June 2010 email said that Mr Michel had had a call from Mr Hunt's adviser, Adam Smith, who said he believed that "the UK government would be supportive throughout the process".

In an email sent on 15 November 2010, Mr Michel told Mr Murdoch "Jeremy" had tried to call him but had received "very strong legal advice not to meet us today as the current process is treated as a judicial one".

"My advice would be not to meet him today as it would be counter-productive for everyone, but you could have a chat with him on his mobile which is completely fine, and I will liaise with his team privately as well," he wrote.

Media playback is unsupported on your device Media caption James Murdoch was pressed over emails from Jeremy Hunt's office

In another email - on 23 January 2011 - Mr Michel said: "He wants us to take the heat, with him, in the next 2 weeks".

He continued: "He very specifically said that he was keen to get to the same outcome and wanted JRM to understand he needs to build some political cover on the process."

The next day Mr Michel told Mr Murdoch he had managed to get some information on Mr Hunt's statement on the BSkyB bid to Parliament due the next day "although absolutely illegal..>!".

Mr Murdoch told the inquiry that the reference had been a "joke". "I think the 'greater than' and the exclamation point there are a wink - it's a joke," he said.

Mr Michel's written submissions to the inquiry suggested that he never had direct contact with Mr Hunt, despite giving the impressions in emails that he had.

He explained that the "JH" or "he" in his emails were shorthand for Jeremy Hunt's team.

Mr Jay suggested that liaising with Mr Hunt via Mr Michel was a way of avoiding the appearance of inappropriate informal contact over the bid.

But Mr Murdoch said that it was "acceptable and part of the process".

'Interests of Murdochs'

After Mr Murdoch's evidence to the inquiry on Tuesday, Prime Minister David Cameron said that he had "full confidence" in Mr Hunt.

It was one of the most dramatic days so far in the long drawn-out inquiry - and it heralds several more

But Mr Miliband said Mr Cameron was "out of touch" and that if Mr Hunt refused to resign he should "show some leadership and fire him".

"Jeremy Hunt should have been standing up for the interests of the British people. In fact it now turns out he was standing up for the interests of the Murdochs," Mr Miliband told the BBC News Channel.

"He himself said that his duty was to be transparent, impartial and fair. But now we know he was providing advice, guidance and privileged access to News Corporation."

Labour deputy leader Harriet Harman also said Mr Hunt should resign, telling the Commons that his conduct had fallen "woefully short" of the standard expected.

She told the BBC News Channel that evidence at the Leveson Inquiry showed Mr Hunt had contact with News International when he was supposed to be acting in a quasi-judicial role for the public interest.

"Jeremy Hunt should have said 'sorry I can't take on responsibility for taking on this decision because I've already nailed my colours to the mast, I've already said I'm in favour of it and I've already had behind the scenes meetings and discussions'."

In the House, Labour former culture secretary Ben Bradshaw raised a Commons point of order to demand Mr Cameron also appear before MPs.

Ofcom review

Mr Murdoch told the inquiry News Corp had been "alive to the risk" that politics might influence his company's position but that he would not expect News Corp's interests to be helped by its support for politicians.

Analysis James Murdoch may have been in the witness box. It is Jeremy Hunt who is feeling the heat. The charge sheet being compiled by his opponents on the basis of the evidence is that the Culture Secretary was meant to have been an impartial judge of News Corporation's now abandoned bid to take full control of BSkyB, Instead, they argue - echoing what was said in court more than once - he was a cheerleader for News Corp. The emails show Mr Murdoch's firm repeatedly gained insight into Mr. Hunt's reported thinking. It was suggested Mr Murdoch had received confidential and covert government information. He insisted nothing inappropriate had taken place. Asked whether he thought Jeremy Hunt had fulfilled his quasi judicial role, Mr Murdoch replied, "I can't say he didn't". Others have reached a different conclusion. Follow @BBCPeterHunt

"That is absolutely not the case and the question of support of an individual newspaper for politicians one way or another is not something that I would ever link to a commercial transaction like this," he said.

"Nor would I expect that political support one way or another ever to translate into a minister behaving in an appropriate way, ever. I simply would not do business that way."

The inquiry revealed that it had taken just seven minutes for News Corp to check with Mr Hunt or one of his advisors a September 2010 blog post by BBC business editor Robert Peston that Ofcom was expected to review News Corp's bid for the remaining BSkyB shares.

And Mr Murdoch said he discussed the BSkyB bid with Mr Cameron at the home of former News International chief executive Rebekah Brooks on 23 December 2010 - seven months after Mr Cameron became prime minister.

The dinner was held two days after Mr Cable was stripped of his responsibility for overseeing the BSkyB bid.

Mr Murdoch said he had spoken briefly to the prime minister about the removal of Mr Cable, saying it was a "tiny conversation" and not a discussion.

He denied the purpose of the meetings with Mr Cameron was partly to find out where he stood on issues which would directly affect Mr Murdoch's companies, such as TV and press regulation.

A spokesman for the prime minister's office said Mr Cameron stood by comments that he had had no inappropriate conversations with James Murdoch about the BSkyB bid and "had done nothing wrong."

Mr Murdoch added that he had been to Chancellor George Osborne's grace-and-favour home Dorneywood once, and had had one discussion with Mr Osborne about the BSkyB bid.

Meanwhile, Scottish First Minister Alex Salmond has strongly denied claims made at the inquiry he offered to lobby the UK government over News Corp's plan to take control of BSkyB.

Mr Murdoch resigned from News International in February 2012.

His father, News Corporation head Rupert Murdoch, will appear before the inquiry on Wednesday and Thursday.

Email after email contains apparently confidential information about announcements Mr Hunt was planning to make about the bid Follow @Peston on Twitter

The inquiry is also tackling the Murdochs' awareness of allegations that the practice of illegally intercepting voicemails went beyond News of the World royal reporter Clive Goodman, who was jailed in 2007.

The third module of the Leveson Inquiry is focusing on the relationship between the press and prominent politicians as part of its examination of the ethics, culture and practices of the UK's newspapers.

The inquiry, led by Lord Justice Leveson, was set up after outrage following allegations that the now-closed News of the World hacked into the voicemail of murdered schoolgirl Milly Dowler.