Giving evidence to the Commons culture, media and sport select committee, Crone said that the email, known as the "for Neville" email, was discussed with News International chairman James Murdoch and "it was the reason that we had to settle the case".
Colin Myler, the final editor of the News of the World before the Sunday tabloid was shut down in July, also told MPs that the email was discussed.
In July, James Murdoch and his father Rupert said in a culture committee hearing that when a payment of almost £700,000 was signed off to phone hacking victim Gordon Taylor, it was done without all the facts being known.
However, Crone and Myler later released a statement saying they did inform him of the email, and their oral evidence today is widely expected to result in James Murdoch being recalled to answer more questions from the MPs.
The Commons committee also quizzed former legal director John Chapman and human resources director Daniel Cloke in a second round of questioning on phone hacking.
The suggested discrepancy in James Murdoch's evidence hinges on a key message sent in April 2008, known as the "for Neville" email due to its connection to the News of the World's former chief reporter Neville Thurlbeck.
When the email was sent, the paper's royal editor Clive Goodman had already been jailed for hacking into the phones of members of the royal household. The News of the World insisted that the practice was down to just one "rogue reporter", but the "for Neville" email is thought to have implied that Thurlbeck was also implicated in malpractices.
Giving evidence to the MPs, Crone said: "[The email] was the reason that we had to settle the case [with Taylor]. And in order to settle the case we had to explain the case to Mr Murdoch and get his authority to settle.
"So certainly it would certainly have been discussed. I cannot remember the detail of the conversation. And there isn't a note of it.
"The conversation lasted for quite a short period, I would think probably less than 15 minutes or about 15 minutes. It was discussed. But exactly what was said I cannot recall."
However, Crone said that there was no "cover-up" by News of the World owner News International, as the "for Neville" email had been provided to them by the Metropolitan Police after it was seized from private investigator Glenn Mulcaire (above right), who was jailed in 2003.
He said that his priority at the time was to avoid more legal cases being launched by four other individuals whose phones Mulcaire had admitted to hacking.
"The imperative or the priority at the time was to settle this case, get rid of it, contain the situation as far as four other litigants were concerned and get on with our business," Crone added.
Labour MP and committee member Tom Watson has already called for James Murdoch to clarify his evidence, but the News Corp executive has said that he "stands by his testimony".
Meanwhile, Steve Coogan has said that he was motivated to take legal action on phone hacking at the News of the World after seeing the paper's former editor Andy Coulson "at the heart of power" as David Cameron's communications chief.