Culture Secretary Jeremy Hunt has refused to back News Corporation chairman and chief executive James Murdoch as a "fit and proper person" to run a media organisation.
MPs this week revealed new evidence suggesting Mr Murdoch was aware of the extent of the News of the World (NoW) phone hacking scandal earlier than was first thought.
Mr Murdoch, who is also non-executive chairman of broadcaster BSkyB, is due to appear before the Culture, Media and Sport Select Committee for a second time next Thursday.
His suitability for his role at BSkyB was on Thursday questioned by Labour MP Chris Bryant.
Speaking at Culture Questions in the Commons, he asked Mr Hunt: "In 2007 News International (the NoW's parent company) lawyers, as we have very recently learned, wrote explicitly to senior management at the News of the World, including to James Murdoch, to make clear the 'sole rogue reporter' line was completely and utterly untrue.
"Does the Secretary of State really believe, with the AGM of BSkyB coming up on November 29, that James Murdoch is therefore a fit and proper person to be chairing that company any longer?"
Media regulator Ofcom operates a "fit and proper person" test for broadcast licence holders.
Mr Hunt told the Commons: "The most important thing is that the truth comes out. James Murdoch is speaking to the select committee, we have the public inquiry by Lord Justice Leveson and we have extensive police inquiries.
"Before those are complete it would not be appropriate for me to make specific comments about who should do what job."