Labour MP Tom Watson said he was contacting Scotland Yard after two former senior executives at the paper publicly contradicted Mr Murdoch's evidence to the Commons Culture, Media and Sport Committee earlier this week.
If the allegations by former editor Colin Myler and former legal manager Tom Crone were correct, he said, Mr Murdoch could face investigation for conspiracy to pervert the course of justice.
"I think this is the most significant moment of two years of investigation into phone hacking," he told the BBC.
"If their version of events is accurate, it doesn't just mean that Parliament has been misled, it means the police have another investigation on their hands."
Prime Minister David Cameron said Mr Murdoch had "questions to answer in Parliament", and suggested that the management of the Murdochs' media empire was now "an issue for the shareholders".
Mr Murdoch, the head of News Corp in Europe and Asia, said he stands by the evidence he gave when he appeared with his father Rupert Murdoch before the committee on Tuesday.
He told MPs he had been unaware of an email suggesting hacking at the paper was more widespread than had been admitted when he signed off a reported £700,000 out-of-court settlement with Gordon Taylor, the chief executive of the Professional Footballers' Association, in 2008.
But in a statement last night, Mr Myler and Mr Crone said Mr Murdoch was "mistaken" and that they had informed him of the email, which had been obtained by Mr Taylor's lawyers.
Mr Watson, a member of the committee and a leading critic of the Murdochs, said that if Mr Myler and Mr Crone were right, Mr Murdoch would have "bought the silence" of Mr Taylor.
"It shows that 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 Gordon Taylor and that could mean that he is facing investigation for perverting the course of justice," he said.
Scotland Yard confirmed it had received a letter from Mr Watson asking detectives on the Operation Weeting inquiry into phone hacking to investigate. A spokesman said that it was "being considered".
Meanwhile, Mr Cameron, speaking on a visit to Warwickshire, said News International - News Corp's UK newspaper publishing arm - needed to clear up the "mess" that had been created.
"Clearly, James Murdoch has got questions to answer in Parliament and I am sure that he will do that. And clearly, News International has got some big issues to deal with and a mess to clear up," he said.
"That has to be done by the management of that company. In the end, the management of a company must be an issue for the shareholders of that company."
Labour MP Chris Bryant, who is taking legal action over claims that his phone was hacked, sought to step up the pressure on the company with a call for the suspension of Rupert and James Murdoch from their roles in News Corp.
In a letter to non-executive directors, he said there had been a "complete failure to tackle the original criminality at the company" and "the lackadaisical approach to such matters would suggest that there is no proper corporate governance within the company".
The email at the centre of the latest controversy - known as the "for Neville" email, apparently in reference to the paper's then chief reporter Neville Thurlbeck - contained transcripts of hacked phone messages.
Critics of News International say it shows that, at the time of the settlement with Mr Taylor, it was known within the company that the practice was not confined to former royal editor Clive Goodman and private investigator Glenn Mulcaire, who had been jailed the previous year.
The company has consistently maintained that it only learned the problem was wider from papers lodged in a civil court case brought by the actress Sienna Miller at the end of last year.
In further developments, the Law Society disclosed that solicitors had been warned by police that their phones might have been hacked by the News of the World.
"Hacking into solicitors' phones would be very serious indeed, and we urge the police to carry out a full investigation," said the society's chief executive, Des Hudson.
At the same time, the Solicitors Regulation Authority announced it was launching a formal inquiry into the role of solicitors in the events surrounding the phone-hacking scandal.
PA
