The two senior News International figures said Mr Murdoch was "mistaken" when he claimed he was not shown an email containing evidence of phone hacking.
The "For Neville" email refers to Neville Thurbeck, the paper's chief reporter, and was sent by Glenn Mulcaire, the private investigator hired by the News of the World to intercept voicemail messages.
It is at the heart of the scandal as it appears to show that News International was aware that phone hacking was more widespread than a single "rogue reporter".
Mr Crone and Mr Myler say they showed the email to Mr Murdoch before he sanctioned the decision to pay £700,000 to Gordon Taylor, the chief executive of the Professional Footballers Association, after Mr Taylor claimed his phone had been hacked.
Mr Murdoch told the Culture, Media and Sport Select Committee that it was "a matter of deep regret" that he had not been shown the email before making the decision. News International said he stood by his testimony.