Lib Dem Simon Hughes joins call for Jeremy Hunt inquiry
Deputy leader Simon Hughes has become the first senior Liberal Democrat to join calls for an inquiry into whether Culture Secretary Jeremy Hunt breached the ministerial code of conduct.
Downing Street says there are no plans to investigate the contact between News Corp and Mr Hunt's ex-special adviser.
Mr Hughes said he could not understand why the issue was not being referred to the independent watchdog.
Employment Minister Chris Grayling said only "half the story" had been told.
On Wednesday, Mr Hunt's special adviser Adam Smith resigned over the extent of his contact with News Corporation during its planned takeover of satellite broadcaster BSkyB.
Mr Hunt, who was responsible for Mr Smith's actions under the ministerial code of conduct, has said he "strictly followed due process", and denied that News Corp had had any "back channel" of influence with his office, which had to rule on the bid.
Mr Hughes said on the BBC's Question Time on Thursday that at the moment he did not think Mr Hunt should resign.
But he added: "What I cannot understand is why the matter of the ministerial code of conduct is not something the prime minister immediately should refer to the person who's been given the job to do it.
"Only the prime minister can do that. He has so far, I gather, resisted doing it. I don't think it gets in the way of the Leveson Inquiry and the evidence - it's a separate matter.
"I don't know why he hasn't done it but I would have thought, to give confidence in the system, I hope the prime minister reconsiders his view.
"That must be in Jeremy's interest. If Jeremy is correct in what he's said, he'll be vindicated. If he's not, then he has to take the consequences."
Mr Hughes said there were "severe questions" Mr Hunt had not yet answered.
Details of the contact between Mr Smith and News Corp emerged in a series of emails seen by the Leveson Inquiry, which is examining press standards and practices.
Speaking on Question Time, Mr Grayling said: "What we've got now is half the story.
"We've got a collection of emails released by a [News Corp] PR man to his bosses - which we know contain plenty of spin because they suggest that he had had meetings and discussions with Jeremy Hunt that he now accepts he hadn't had.
"That's the only evidence that's out there."
Shadow culture secretary Harriet Harman has written to the prime minister calling for him to get his independent adviser on ministerial conduct, Sir Alex Allan, to launch an inquiry into whether Mr Hunt breached the ministerial code.
Labour leader Ed Miliband said it was impossible to believe that Mr Smith had "acted as a lone wolf" and the party has called for the culture secretary to resign.
Mr Hunt told the Commons that Permanent Secretary Jonathan Stephens had approved Mr Smith's role as liaison on the BSkyB deal.
But when Mr Stephens appeared before the Public Accounts Committee for a session on the Olympics, he repeatedly refused to be drawn about whether that was the case.
He was asked at least 10 times, but referred the MPs to previous statements made by Mr Hunt and Mr Smith, and said he had been "given no notice" of the MPs' questions.
The prime minister's spokesman said he was sure Mr Hunt had acted properly and it was a matter for the Leveson Inquiry.
Mr Hunt's handling of News Corp's takeover bid for BSkyB was raised at the Leveson Inquiry on Thursday as Rupert Murdoch gave evidence for a second day.
The News Corp chairman denied that he thought Mr Hunt had been "on our side", saying that the minister had extracted "very big concessions" from the company.
Meanwhile, the broadcast regulator Ofcom has stepped up its inquiry into whether BSkyB is a fit-and-proper company to hold a broadcast licence.
It has asked News Group newspapers - owned by News Corp - for more documents disclosed in the civil cases relating to phone hacking.