David Cameron says James Murdoch “clearly” needs to answer questions in Parliament after his evidence on phone hacking was challenged.
Labour MP Tom Watson has asked police to investigate after Mr Murdoch’s evidence to MPs was disputed by two ex-News of the World executives.
Mr Murdoch said he was not “aware” of an email suggesting hacking went wider than a single “rogue” reporter.
But ex-NoW editor Colin Myler and legal manager Tom Crone said they told him.
Mr Murdoch later said he stood by the evidence he gave the culture committee on Tuesday.
Following Thursday’s statement by Mr Myler and Mr Crone, committee chairman John Whittingdale said Mr Murdoch had agreed to write to the committee on various points he had been unable to address at the hearing.
He said: “I’m sure if the statement suggests there’s conflict between what Colin Myler is saying and what he said, we will ask him to answer that as well.”
Speaking during a visit in Warwickshire, the prime minister said: “Clearly James Murdoch has got questions to answer in Parliament and I’m sure he will do that.
“And clearly News International has got some big issues to deal with and a mess to clear up, that has to be done by the management of that company.
“In the end the management of the company must be a matter for the shareholders of that company, but the government wants to see this sorted out.”
Mr Watson said he was going to formally bring the matter of James Murdoch’s disputed evidence to the attention of Deputy Assistant Commissioner Sue Akers, who is leading Operation Weeting, the investigation into phone hacking.
The Metropolitan Police later confirmed Mr Watson’s request for an investigation into the disputed evidence “was being considered”.
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Labour MP Tom Watson: “This is the most significant moment of two years of investigation into phone hacking”
The West Bromwich MP told the BBC: “This is the most significant moment of two years of investigation into phone hacking.
“If [Colin Myler and Tom Crone’s] statement is accurate it shows James Murdoch had knowledge that others were involved in hacking as early as 2008, it shows he failed to act to discipline staff or initiate an internal investigation, which undermines Rupert Murdoch’s evidence to our committee that the company had a zero tolerance to wrongdoing.”
The MP added: “More importantly, it shows he not only failed to report a crime to the police but because there was a confidentiality clause involved in the settlement it means that he bought the silence of [chief executive of the Professional Footballers Association] Gordon Taylor and that could mean he is facing investigation for perverting the course of justice.”
He said: “There is only going to be one person who is accurate. Either James Murdoch, who to be fair to him is standing by his version of events, or Colin Myler and Tom Crone.”
“Myler and Crone will have to answer for themselves. They are clearly concerned that they have effectively been hung out to dry by James Murdoch in the evidence session earlier in the week.”
At the committee hearing on Tuesday, Labour’s Tom Watson asked Mr Murdoch: “When you signed off the Taylor payment, did you see or were you made aware of the full Neville (Thurlbeck) email, the transcript of the hacked voicemail messages?”
Mr Murdoch replied: “No, I was not aware of that at the time”.
He went on: “There was every reason to settle the case, given the likelihood of losing the case and given the damages – we had received counsel – that would be levied.”
In their statement issued on Thursday Mr Myler and Crone said: “Just by way of clarification relating to Tuesday’s CMS select committee hearing, we would like to point out that James Murdoch’s recollection of what he was told when agreeing to settle the Gordon Taylor litigation was mistaken.
“In fact, we did inform him of the ‘for Neville’ email which had been produced to us by Gordon Taylor’s lawyers.”
In a statement issued by News Corporation, James Murdoch said: “I stand by my testimony to the select committee.”
Meanwhile Labour MP Chris Bryant, who is suing over allegations his phone was hacked, has called for the James and Rupert Murdoch to be suspended by News Corp’s board.
In a letter to the non-executive directors of the firm, he said Rupert Murdoch’s refusal to accept responsibility for what happened at the News of the World “would suggest that there is no proper corporate governance within the company”.
Meanwhile, Deputy Prime Minister Nick Clegg has confirmed he did raise questions about Mr Cameron’s decision to bring Andy Coulson into Number 10.
He told the BBC: “Of course I talked to Cameron about it because before the election we were constantly saying, as a party, ‘what’s going on?’, ‘This doesn’t look good’ and so on.”
“But as Cameron has said himself, it was his decision and he said ‘I have received the assurances I sought’ and on that basis I want to give Andy Coulson a second chance and that’s his decision.”
“Of course I raised it, of course I questioned it, of course we talked about it.”
The BBC has also learned the FBI plans to contact actor Jude Law following claims his mobile phone was hacked during a visit to the US.
It is alleged a story published by the News of the World in 2003 was based on information obtained from his voicemail which, if proved, could lead to charges in the US because his phone would have been operating on a US network. News International denies the claims.