James Murdoch appearing before the culture, media and sport committee with his father RupertCredit: PA
Earlier today (29 July), the committee outvoted MP Tom Watson who was calling for Murdoch to be immediately recalled, after the accuracy of some of his evidence was disputed.
Former News of the World editor Colin Myler and lawyer Tom Crone issued a joint statement last week claiming Murdoch's account of an email said to suggest hacking was more widespread, was "mistaken".
"In fact, we did inform him of the 'for Neville' email which had been produced to us by Gordon Taylor's lawyers", they said at the time.
However, in a letter published by the committee today, Murdoch said he stood by his statement and had "answered truthfully".
The committee is now writing to Murdoch, Myler and Crone, to ask for more details.
In an interview with BBC Radio 4 The World At One, committee chair John Whittingdale added it is quite likely, following written evidence, they will all be called to appear before the committee.
"At the moment we only have the sketchiest details over the ways evidence was incorrect," he said.
"We have heard from the press statement given by Colin Myler and Tom Crone that they dispute the evidence … but we need more detail where and in what way they dispute it. And once we have that obviously that will raise questions we will wish to put".
He added: "I think we will almost certainly want to hear from Colin Myler and Tom Crone, particularly since evidence they previously gave two years ago seems completely contradictory to what is being said now.
"And at the same time, if they do dispute the evidence James Murdoch gave, it is very possible we may wish to call Murdoch back to address that."
Also in today's The World At One programme, a former detective chief inspector who worked on the Sarah Payne investigation said he believes his phone was also hacked.
Martyn Underhill told the BBC he contacted Operation Weeting just over two weeks ago to report his suspicion.
The follows the news that Sara Payne, the mother of murdered schoolgirl Sarah Payne, has been contacted by police to say her details had been found among documents seized from private investigator Glenn Mulcaire.