A Labour frontbencher has claimed a "criminal offence" may have been committed if News International was handed information about its BSkyB bid by Jeremy Hunt's office.
Chris Bryant, a shadow immigration minister, told the BBC's Sunday Politics programme that the Prime Minister had to turn the affair over to Sir Alex Allan, his independent adviser on the ministerial code.
He said Lord Justice Leveson had made it clear he would not rule on whether Mr Hunt broke the ministerial code during his handling of the £8 billion BSkyB bid.
Labour has called for Mr Hunt to resign in the wake of publication by the Leveson Inquiry of emails between News International lobbyist Fred Michel and Adam Smith, a special adviser to Mr Hunt. Mr Smith quit his post after the revelations last month.
Mr Bryant, MP for Rhondda, told the programme: "The point nobody can run away from in either Downing Street or Jeremy Hunt's office is the fact that every element Fred Michel predicted the Secretary of State would say, he did say.
"News International knew information about what the Secretary of State was going to say before he said it, and also before commercial operators did. That's a criminal offence, a straight-forward criminal offence."
A Department for Culture, Media and Sport spokesman said: "Jeremy Hunt will respond fully to all allegations on his conduct when he gives his evidence to the Leveson Inquiry in due course. He is confident that his evidence will vindicate the position that he has behaved with integrity on every issue.
"It has already been made clear that when Fred Michel has claimed in emails to be speaking to Jeremy Hunt, that was not the case."
Prime Minster David Cameron has said Mr Hunt should be allowed to give his evidence to the Leveson Inquiry before any judgment is made on whether he has broken the ministerial code.
Fresh allegations emerged last week during Rebekah Brooks's evidence at the inquiry, when a further email from Mr Michel was published suggesting Mr Hunt wanted News International to "guide his and Number 10's positioning" on the phone hacking scandal.