ALEX Salmond today faces growing pressure to "come clean" over claims he offered to lobby on behalf of Rupert Murdoch, as David Cameron fights to save Culture Secretary Jeremy Hunt who is embroiled in the BskyB takeover row.

The First Minister brushed aside opposition demands that he make an emergency statement to the Scottish Parliament, insisting he would go ahead with a planned speech to the Institute of Directors' conference in London today, near where the News Corporation chairman will be giving evidence to the Leveson Inquiry.

It follows the publication of emails by Frederic Michel, the director of public affairs at News Corp. He told Mr Murdoch's son James, one of the company's chief executives who gave evidence to the inquiry into media standards: "I met with Alex Salmond's adviser today. He will call [Jeremy] Hunt whenever we need him to."

In another email, Mr Michel referred to a "very good dinner" between the Mr Salmond and the editor of the Scottish Sun, which had decided to back the SNP at the Holyrood elections. He wrote: "Alex was keen to see if he could help smooth the way for the process."

Johann Lamont, the Scottish Labour leader, said the whole affair "stinks". She added: "It seems all that mattered to Salmond was that he would support Murdoch in return for Murdoch's papers supporting Salmond."

Willie Rennie, the Scottish Liberal Democrat leader, demanded the First Minister go before MSPs to explain his actions, while David McLetchie, the former Scottish Conservative leader, accused him of "conduct unbecoming of a First Minister".

However, a spokesman for Mr Salmond denied any wrongdoing and said the emails simply represented "internal chatter from within News International". He went on: "It is total nonsense to suggest there was ever any quid pro quo offered by the Scottish Government over the BSkyB bid - because the Scottish Government had absolutely no determination over BSkyB's ownership."

The spokesman made clear the First Minister had never spoken to or corresponded with Mr Hunt on this issue and referred to James Murdoch's own denial of Scottish Government lobbying on News Corp's behalf.

Mr Murdoch told the inquiry: "If the insinuation is that there was any quid pro quo with editorial coverage versus a commercial agenda, I can tell you categorically that it's false."

Mr Salmond's spokesman also revealed yesterday the First Minister would be giving evidence to the inquiry. He had been invited "some time ago" but it had not been mentioned before because no date had been set. Mr Salmond is expected to appear in the next few weeks.

The latest row comes on top of what the the First Minister's critics regard as an unhealthy closeness between the SNP leader and Mr Murdoch senior, who earlier this year described Mr Salmond on Twitter as "clearly most brilliant politician in UK".

If the Murdoch row were not enough, the First Minister is expected to come under fire today from Donald Trump. The US tycoon, angry at the prospect of offshore wind turbines near his luxury golf course in Aberdeenshire, is due to tell a Holyrood committee that wind power will wreck tourism, having already accused Mr Salmond of being "hell bent on destroying Scotland's coast and therefore Scotland itself".

Meanwhile, at Westminster, the Prime Minister is under intense pressure on the back of Mr Michel's emails which suggested Mr Hunt – who had a quasi-judicial role to determine the BSkyB takeover issue – was secretly backing the Murdoch empire's bid. In one email, the News Corp PR chief noted: "He [Hunt] said we would get there at the end and he shared our objectives."

As Mr Cameron expressed his full confidence in Mr Hunt, the Culture Secretary defied Labour calls to

resign. He insisted he had conducted the process of deciding whether to approve the BSkyB bid with "scrupulous fairness" and wrote to the Leveson inquiry asking for an early date to give evidence.

He said: "Now is not a time for knee-jerk reactions. We've heard one side of the story but some of the evidence reported meetings and conversations that simply didn't happen. Rather than jump on a political bandwagon, we need to hear what Lord Justice Leveson thinks after he's heard all the evidence."

Today, Ed Miliband is set to intensify the pressure on the PM at Commons question time. Last night, the Labour leader accused Mr Hunt of "standing up for the interests of the Murdochs" instead of standing up for the British people.

Mr Miliband added: "He said his duty was to be transparent, impartial and fair in the BSkyB takeover, but now we know he was providing advice, guidance and privileged access to News Corporation. He cannot stay in his post and if he refuses to resign, the Prime Minister must show leadership and fire him."

Later, in the Commons, Margaret Curran, Shadow Scottish Secretary, called on Scottish Secretary Michael Moore to come to the chamber and outline the implications for Scotland of the claims of lobbying against Mr Salmond.