Culture Secretary Jeremy Hunt has attempted to fight back against demands for his resignation, telling MPs he had dealt with News Corporation's bid to buy BSkyB with "scrupulous fairness".
But his special adviser Adam Smith quit his job, admitting that he "went too far" in communications with the company's chief lobbyist Frederic Michel.
Labour said that evidence released by the Leveson Inquiry into media standards indicated that Mr Hunt had breached the ministerial code, and urged David Cameron to refer the case to his independent adviser on ministers' conduct, Sir Alex Allen.
Ed Miliband said the affair has left "a shadow of sleaze" over the Government, but the Prime Minister made clear he still has confidence in his Culture Secretary, telling MPs Mr Hunt had "my full support for the excellent job that he does".
Mr Cameron had a private meeting with the Culture Secretary on Tuesday night, after the release of a 163-page dossier containing scores of emails from Mr Michel detailing his contacts with Mr Hunt's office during the bid process. The PM's official spokesman declined to reveal details of their conversation, but said that Mr Hunt had at no point offered to resign.
Labour said the emails showed Mr Hunt acted as a "back-channel" for the Murdochs, passed secret information to News Corp, and misled Parliament over the extent of his contacts with the company at a time when he held a quasi-judicial responsibility for determining whether the £8 billion bid should go ahead.
But Lord Justice Leveson warned against jumping to conclusions, telling the inquiry: "I am acutely aware from considerable experience that documents such as these cannot always be taken at face value, and can frequently bear more than one interpretation."
Mr Hunt told the Commons that it was "categorically not the case" that the emails were evidence that a back channel existed for News Corp to influence his decision. "They did not influence my decision in any way," he told MPs.
Labour deputy leader Harriet Harman on Wednesday night wrote to Mr Cameron identifying what she said were three specific breaches of the ministerial code by Mr Hunt. They were failing to take responsibility for a special adviser, disclosing the contents of a parliamentary statement to News Corp before informing MPs, and failing to give "accurate and truthful" information to Parliament on the release of communications between his department and News Corp.
"These must now be referred to the independent adviser on ministers' interests as a matter of urgency," she said.