James Murdoch will face another grilling from MPs if Labour backbencher Tom Watson gets his way.
Mr Watson said he wanted further evidence from the News International chairman over the question of whether he was aware that phone-hacking at the News of the World newspaper was widespread.
Colin Myler, the last News of the World editor, and Tom Crone, a former lawyer at News International, had claimed Mr Murdoch was wrong to deny he knew about an email proving the practise went beyond 'one rogue reporter'.
The email, sent to News of the World's chief reporter Neville Thurlbeck, outlined proposals for an out-of-court settlement with Professional Footballers' Association chief executive Gordon Taylor.
Mr Watson said invitations would be issued shortly to "get to the bottom of this". He confirmed reports that Mr Crone and Mr Myler would also be invited to give evidence.
Parliament will not return from its summer recess until September, meaning the hearings will not be able to take place until then.
Mr Murdoch faced a two-hour grilling from BSkyB's board, which he and his father Rupert Murdoch have a 36% stake in.
There had been speculation that the phone-hacking scandal could see his position come under pressure, but the board unanimously backed him.
"Whilst I do appreciate there's a lot of noise around events at News International... our job as a board is to focus on delivering for our customers," chief executive Jeremy Darroch told Sky News.
"That's what we're in business to do. The board was unanimous that James should continue to lead that as chairman."
The company has decided to offer a £750 million payout to shareholders after registering both a 15% fall in share value in the last month and a 15% fall in annual profits.
"Sky has had an excellent year of delivery for both customers and shareholders," Mr Darroch said.
"We have stayed focused on executing our plan and customers have responded by rewarding us with more of their business.
"Today's announcement of a capital returns programme is a reflection of our strong performance and financial position, which flow directly from delivering for customers in the marketplace."
Despite being hit by the failed £10 billion takeover bid from the Murdochs' News International, BSkyB remains highly profitable. It saw a 23% increase in operating profits and is consolidating its position as a market leader in customers taking broadband, telephone and pay-TV.