Jeremy Hunt is under renewed pressure after the UK's former top civil servant insisted he should have been clear what discussions his special adviser could have with News Corporation over its bid for BSkyB.
Lord O'Donnell also said he believed David Cameron's links to Rupert Murdoch's media empire had been too close.
The comments, in evidence to the Leveson Inquiry, came as Commons Speaker John Bercow demanded the Culture Secretary answer questions from MPs over his conduct in the row.
The Government has previously argued that critics should wait for a full explanation when Mr Hunt makes his own appearance as a witness.
Lord O'Donnell - who retired as Cabinet Secretary at the end of last year - was asked about email exchanges between Mr Hunt's special adviser Adam Smith and News Corp lobbyist Fred Michel.
Mr Smith resigned last month after admitting that the discussions, which included previews of statements the secretary of state was due to make to parliament, had gone too far.
"It's clear in the special advisers' code (of conduct) that in terms of authorisation ministers should authorise their special advisers as to what they should do, for example with the media," the peer said. "I would have expected the minister to be clear as to what he thought the special adviser should have been doing."
He also insisted "all parties" should have been kept informed about the progress of scrutinising the News Corp bid for BSkyB.
"Talking about process is fine," he said, "but you should make sure that the same information is passed on to all parties in a case... so fairness is absolutely crucial to what happened."
A spokesman for the Department for Culture, Media and Sport said there was "no question" of Mr Hunt failing to fulfil his obligations to Parliament, adding: "Jeremy Hunt will submit his evidence to the Leveson Inquiry as planned and this evidence will be made public as part of the Leveson process."