James Murdoch could be asked to clarify his evidence to the Commons Culture, Media and Sport Committee, chairman John Whittingdale said.
His remarks came after claims from two former senior News International staff that the company’s chairman had been “mistaken” in Tuesday’s hearing, which he attended with his father Rupert.
Mr Murdoch junior told the committee he was “not aware” of an email suggesting the practice of phone hacking at the News of the World went wider than one rogue reporter.
But in a statement issued last night, former News of the World editor Colin Myler and former News International legal manager Tom Crone said they had informed Mr Murdoch of the email.
Conservative MP Mr Whittingdale said he had not seen the statement, but that Mr Murdoch had already agreed to write to the committee on various points he had been unable to immediately address at the hearing.
He told the Press Association: “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.”
He stressed that the committee would not be recalled on the matter.
The issue hinges on a settlement paid to Professional Footballers’ Association chief executive Gordon Taylor in 2008, worth a reported £700,000, after he brought a damages claim against the News of the World.
At the committee hearing, committee member Tom Watson asked James Murdoch: “When you signed off the Taylor payment, did you see or were you made aware of the full Neville e-mail, the transcript of the hacked voicemail messages?”
He replied: “No, I was not aware of that at the time.”
He went on to say: “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, Mr Myler and Mr 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, James Murdoch said: “I stand by my statement to the select committee.”
Meanwhile, News International has confirmed that a member of staff was sacked yesterday in relation to his previous work at the News of the World.
In another development, former News of the World assistant editor Greg Miskiw said he was returning to the UK voluntarily from his current home in Palm Beach, Florida.
Earlier, Nick Clegg said media watchdogs should consider “very seriously” whether News Corporation remains a fit and proper organisation to run satellite TV company BSkyB.
In an end-of-term press conference in Westminster, Mr Clegg said Ofcom should apply the test “on an ongoing basis” to ensure that companies remain fit to hold broadcasting licenses.
The Deputy Prime Minister said the phone-hacking scandal had uncovered “murky practices and dodgy relationships” at the heart of Britain’s establishment, and said Lord Justice Leveson’s inquiry provided a “once-in-a-generation” opportunity to clean up the media, politics and the police.
He offered his support to David Cameron, after it emerged that the Prime Minister discussed News Corp’s bid to take over BSkyB in private meetings with executives including chairman Rupert Murdoch and former News International chief executive Rebekah Brooks.
Mr Clegg said Mr Cameron’s assurances in the House of Commons that the discussions on BSkyB were not “inappropriate” and that he did not act as a conduit between News Corp and Culture Secretary Jeremy Hunt “speak for themselves”.
But he stressed that he did not attend the PM’s meetings with News Corp executives and that he led the way in Government in calling for a judge-led inquiry into the hacking claims and for Mr Murdoch to drop the BSkyB bid, as he later did.
Ofcom had confirmed it had the power “to judge whether a media group is fit and proper or not” to hold a broadcasting licence, said Mr Clegg.
He added: “There needs to be evidence quickly that the fitness and properness is applied on an ongoing basis to News International and other media organisations.”
An Ofcom spokesman said it was “conscious of the level of concern” and said it was “meeting with relevant authorities to explain our duty to be satisfied that persons holding broadcasting licences are fit and proper”.
Speaking after days in which the headlines have been dominated by Mr Murdoch’s dramatic appearance before MPs and Mr Cameron’s lengthy statement to Parliament, Mr Clegg sought to carve out a distinctive position for the Lib Dems in the hacking row.
Lib Dems came at the issue from “completely different directions” from Conservatives and had a record going back to before the general election of calling for a hacking inquiry and demanding new rules to ensure media pluralism, he said.
Mr Clegg also confirmed he had questioned Mr Cameron’s decision to appoint former News of the World editor Andy Coulson as Downing Street director of communications after the election.
He stressed that it was Mr Cameron’s decision alone to take his media adviser - who quit in January and was later arrested by police investigating the hacking allegations – into the heart of government.
It was confirmed yesterday that Mr Coulson did not have the highest level of security vetting before taking up his Downing Street job.
Unlike Tony Blair’s communications chief Alastair Campbell, who had top-level clearance, Mr Coulson was subjected only to a lower level of vetting, which meant he was not permitted to view the most secret Government files.
Labour backbencher Nick Raynsford said he would seek a meeting with Mr Cameron over claims that a senior civil servant’s phone was hacked while Mr Coulson was employed in Downing Street.
The Cabinet Office firmly denied the claim, made by the Greenwich and Woolwich MP in the House of Commons.
But Mr Raynsford told the Press Association that the individual concerned “held a very senior position in the civil service” and had been “deeply shocked” to learn of the eavesdropping.
Meanwhile, the FBI planned to contact actor Jude Law following claims that his mobile phone was hacked during a visit to the US, the BBC reported.