London (CNN) -- Britain's Prime Minister David Cameron said Friday that James Murdoch has "questions to answer in Parliament," a day after former top executives of News of the World accused the News Corp. executive of giving "mistaken" evidence.
The claim by the editor of the News of the World at the time it folded on July 10, Colin Myler, and the paper's former head of legal affairs, Tom Crone, related to what Murdoch told a parliamentary committee about a settlement to Gordon Taylor, chief executive of the Professional Footballers Association.
Crone and Myler said they had told Murdoch of an e-mail regarded as central to the question of whether more than one reporter at the paper was involved in illegal activity.
But Murdoch, the son of media mogul Rupert Murdoch, offered contradictory information to the committee, as he, his father and former News Corp. executive Rebekah Brooks were quizzed over a phone-hacking scandal that has shaken public confidence in Britain's media, police and political establishment.
Asked about James Murdoch's suitability to "clean up" News International, Cameron said: "Clearly James Murdoch has got questions to answer in Parliament and I am sure that he will do that, and clearly News International has some big issues to deal with and a mess to clear up."
Cameron, speaking to reporters as he visited an auto plant, said "the government wants to see this sorted out."
The e-mail referred to by Crone and Myler is known as the "for Neville" e-mail, so named for its apparent connection to the News of the World's former chief reporter, Neville Thurlbeck.
It is thought to have played a key role in the decision by executives at News International, which owned News of the World, to pay some £700,000 ($1.1 million) to Taylor in an out-of-court settlement after he threatened legal action, the Guardian reported.
In a statement posted on News Corp.'s website, James Murdoch said, "I stand by my testimony to the select committee."
But Myler and Crone described as "mistaken" James Murdoch's recollection of what he was told when he agreed to settle the Taylor case.
"In fact, we did inform him of the 'for Neville' e-mail which had been produced to us by Gordon Taylor's lawyers," they said in a joint statement.
John Whittingdale, chairman of the committee that held Tuesday's hearing, told CNN that information by Crone and Myler conflicted with what James Murdoch told the committee.
"It's only one point but it's quite an important point because the 'for Neville' e-mail was always regarded by the committee as one of the most important pieces of evidence suggesting there was wider involvement than just one reporter," he said.
That reporter is former royal editor Clive Goodman, the sole journalist for News of the World who has been prosecuted in the phone-hacking scandal.
The Culture, Media and Sport Select Committee expected a written response from James Murdoch on a number of points for which he had not had the information when questioned, Whittingdale said.
"When he responds to the committee, which I expect him to do fairly shortly, I will ask him to address the conflict between his version and theirs, and clarify his remarks. We will wait to see how he responds," Whittingdale said.
The committee will send the letter asking for clarification on the unanswered questions and the "for Neville" e-mail next week. News Corp. has said it will respond promptly, Whittingdale said.
Whittingdale said the committee was "a long way" from reconvening in a special session during Parliament's recess to consider the matter.
Meanwhile, Labour lawmaker Chris Bryant -- who has played a prominent role in the debate over the phone-hacking scandal -- wrote to the nonexecutive directors of News Corp. Friday raising serious concerns over the testimony given by James and Rupert Murdoch and urging that the pair be suspended from their duties.
James Murdoch told the committee on Tuesday that Crone and Myler had not told him about the e-mail when he agreed to approve the settlement with Taylor, which included a proviso of confidentiality.
"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 voice mail messages?" James Murdoch was asked Tuesday by committee member Tom Watson.
"No, I was not aware of that at the time," Murdoch answered.
Asked why he had approved the hefty settlement payment to Taylor, Murdoch said: "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."
Asked whether he felt the Taylor settlement was too high, he said, "Going back and looking at what we knew in 2008, looking at that advice, remembering that advice and looking at the context of the time, if we step back those three years, it was a decision that, given that context, I would still stand by, I think."
Asked what kind of preparation he had had before his testimony, James Murdoch replied, "We were advised, fundamentally, to tell the truth, and to come and be as open and transparent as possible. That is my and my father's intent and intention, and we hope that we can show you that that is what is happening."
Bryant, who believes he, too, is a hacking victim, said the statement from Crone and Myler suggests James Murdoch knew of the e-mail and was not honest with Parliament.
"It is my contention that this further proves the complete inability of News Corporation as an entity and James Murdoch personally to exercise either due diligence or proper corporate control," Bryant's letter says.
"I realise that these are serious allegations, but since the Metropolitan Police have themselves said that News International deliberately thwarted their investigation, I hope you will take these matters far more seriously than seems to have been the case thus far.
The now-defunct News of the World was part of News International, the British arm of Rupert Murdoch's News Corp. media empire.
CNN's Laura Smith-Spark contributed to this report.