Labour has accused Jeremy Hunt of trying to "evade parliament" after Lord Justice Leveson made clear he will not make a judgement on the minister's conduct in the BSkyB takeover bid.
David Cameron has rejected calls for a separate probe into the culture secretary's conduct because the Leveson inquiry, which is investigating the culture, practice and ethics of the press, is already addressing the issue.
Mr Hunt is due to give evidence in court room 73 later this month. But Lord Justice Leveson used a statement this lunchtime to subtly rebuke the prime minister for relying on his inquiry to assess Mr Hunt's conduct.
"I won't be making a judgement on whether there has been a breach of the ministerial code," he said.
The judge went further, underlining that his inquiry was not tasked with establishing the truth in such a dramatic fashion.
"It is not my intention that anyone should be tripped up or trapped," Lord Justice Leveson added.
"There is no cross-examination as such. Those who look for forensic fireworks should turn to fictional trials."
Mr Hunt is under pressure for his office's inappropriate contacts with News Corporation officials as he assessed their bid to takeover BSkyB. His special adviser, Adam Smith, has already resigned over his communications with News Corporation's public affairs executive Frederic Michel.
"It was never the role of the inquiry to do this and the prime minister and Jeremy Hunt should stop trying to hide behind it," shadow culture secretary Harriet Harman said.
She has written to Commons Speaker John Bercow expressing her fear that Mr Hunt is "evading his responsibility to parliament".
"The prime minister and Jeremy Hunt are using every trick in the book to avoid any kind of investigation," Ms Harman added.
"They clearly have something to hide and Jeremy Hunt must resign."
Andy Coulson appearance
Former head of communication in Downing Street Andy Coulson appeared at the Leveson inquiry today, where he admitted relations between the press and politicans had become too close while he was at News of the World and No. 10.
"The prime minister has said it got too cosy and I'm not minded to disagree with him," he said.
"Personal relationships have got in the way of the message, that is abundantly clear".
He also dismissed the idea that Mr Cameron had conspired to make News Corp's bid for BSkyB as easy as possible.
"If there was a deal and there was a conspiracy … why was Vince Cable given the job?" he asked.
"It is in the prime minister's gift to decide who held which brief in his Cabinet."
Mr Coulson admitted recieving severance payments from News International while being employed by the Tory party and that he had access to sensitive information while at No 10 - despite claims to the contrary from the government.
He said Mr Cameron asked him about the phone-hacking conviction of Clive Goodman before he took the job but that senior No 10 figures Ed Llewellyn and Francis Maude did not.
Rebekah Brooks will be appearing at the inquiry tomorrow.