Rupert Murdoch, the News Corporation chairman and chief executive, has been asked to appear before MPs on the Commons culture select committee to answer questions about the phone-hacking scandal along with his son James and News International chief executive Rebekah Brooks.

The culture, media and sport select committee, which has twice published critical reports into the affair, has written to the trio of executives inviting them to appear.

News International said: "We have been made aware of the request from the CMS select committee to interview senior executives and will cooperate. We await the formal invitation."

The committee, chaired by Tory MP John Whittingdale, cannot compel witnesses to appear. But given the gravity of the scandal and the public appetite for an explanation from senior News Corp figures, Murdoch is likely to come under pressure to give evidence to parliament for the first time in his career.

Brooks refused to appear before the select committee when it carried out its second inquiry into phone hacking at the News of the World following Guardian revelations in July 2009 that News International had paid Gordon Taylor and two other hacking victims to drop legal action.

She has answered questions from MPs twice before, apparently telling the home affairs select committee during her first appearance in 2003, when she had just been appointed editor of the Sun, that News International titles had paid police for information.

The company recently issued a statement saying Brooks was not aware of any specific payments to police officers by News International.

The Labour Paul Farrelly MP, who sits on the committee, said: "It's been alleged that some of the people who came to see us as witnesses knew full well that hacking was rife on the news desk at the very least."

The paper's former managing editor Stuart Kuttner, editor Colin Myler and head of legal Tom Crone all gave evidence in 2009 along with Les Hinton, who was chairman of News International. They claimed an internal inquiry had uncovered no evidence that hacking went beyond former royal editor Clive Goodman, who was jailed for hacking into phones in January 2007.

The committee considered calling all four of them again and may still do so after it has heard from the most senior executives at the company, Farrelly said.

The News Corp executives will be given until Thursday to reply in the hope they will appear next Tuesday afternoon, the final day of the current parliament.

Farrelly said James Murdoch "had a lot to amplify" following his statement last week, in which he apologised for approving payoffs to Gordon Taylor and other hacking victims and for giving incorrect information to parliament, saying he had not been fully informed about the extent of News of the World phone hacking at the time.

"It was a mea culpa for the organisation which has been a long time coming but it didn't say who knew what and when and who therefore lied to parliament", he added.

Farrelly said the committee would employ rarely used parliamentary powers to summon Brooks if she refused to appear.

It is understood Brooks could be compelled to attend if a majority of the House of Commons votes in favour of a motion requiring her to do so.

That vote could not realistically take place until parliament reconvenes in the autumn, however.

The committee considered using those powers previously when the News International chief executive said she would not attend the 2009 phone-hacking hearings but was advised by the Commons authorities not to do so.

It is unclear whether the committee can compel Rupert and James Murdoch to appear because they are foreign nationals.

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