Speaking today in Parliament, he denied that the company had any "back channel" influence during the takeover process, including when he acted in a "quasi-judicial" role.
Hunt's special adviser Adam Smith today resigned from his post after a number of explosive email communications emerged from News Corp lobbyist Fred Michel.
In a statement, Smith said that he had gone "too far" in the contact with Michel, but insisted that Hunt had acted "scrupulously fairly" in the arbitration process.
Hunt delivered a statement today following calls for him to step down over a series of emails released at the Leveson Inquiry relating to his handling of the takeover.
The minister said that he had followed "due process" in the Sky bid, including the non-compulsory involvement of regulators Ofcom and the Office of Fair Trading.
However, Labour's Harriet Harman said that he was not judging the bid, but rather 'backing" it, and so should stand down.
"Your conduct should have been quasi-judicial but it fell far, far short of that and short of the standards required by your office," she told Hunt.
News Corp head of public affairs Michel has said that the 'JH' references in his emails were actually shorthand for special adviser Smith, and that he had never actually had any direct contact with the culture secretary.
But referring to the departure of Smith in Parliament today, Labour MP Dennis Skinner told Jeremy Hunt: "When the posh boys are trouble, they sack the servants."
Jeremy Hunt took over arbitration of the £7.5bn Sky takeover in December 2010, despite existing concerns over his impartiality in the bid process.
A month after News Corp submitted its first bid for the remaining shares in Sky that it did not own, Hunt said in an interview with the Financial Times: "It does seem to me that News Corp do control Sky already, so it isn't clear to me that in terms of media plurality there is a substantive change, but I don't want to second guess what regulators might decide."
In his Commons statement, Hunt insisted that he had followed due process, and said that Labour's claim that "there was a back channel through which News Corporation were able to influence my decisions" was "categorically not the case".
Hunt has also confirmed that he has requested to Lord Leveson's inquiry into press standards that his scheduled appearance to give evidence should be brought forward.
"When I present my evidence the public will see that I conducted this process with scrupulous fairness throughout," he added.
Today, David Cameron gave Hunt his "full support", saying that the culture secretary does an "excellent job".
The prime minister also said that it would be wrong to "pre-judge" the outcome of the Leveson Inquiry, and accused Labour of getting on the "political bandwagon".