David Cameron has defended his refusal to launch an investigation into Jeremy Hunt - insisting the Culture Secretary acted “wisely and fairly” and had given “a good account of himself”.

Mr Hunt held on to his job after Downing Street said his evidence to the Leveson Inquiry on Thursday showed he “acted properly” in his handling of the News Corporation bid for BSkyB.

But the Prime Minister is under pressure to launch an investigation into claims that his Cabinet colleague breached the ministerial code.

He also faces questions about his own judgment in appointing Mr Hunt to adjudicate on the proposed takeover despite knowing of his personal sympathies for the Murdoch media empire.

But despite the emergence, in evidence disclosed to Leveson, of pro-bid text messages sent by Mr Hunt on the day he was handed responsibility, Mr Cameron said he had acted entirely properly.

“The advice I was given was that what mattered was not what Jeremy Hunt had said publicly or privately but how he was going to conduct himself during the bid,” he told BBC1's Andrew Marr Show.

“That's how I think we should judge him: did he adjudicate this bid wisely and fairly?

“And he did. He took legal advice at every stage, and he followed that legal advice and he did many things that were not in the interests of the Murdochs or BSkyB and that side of things.

“And I think he gave a good account of himself to the Leveson Inquiry, he's given a good account of himself to Parliament, and I think that's the key point.”

Mr Cameron said he had “looked carefully” at pro-Murdoch public statements made by Mr Hunt and taken legal advice before transferring bid responsibility to him from Vince Cable.

The Business Secretary was stripped of the media role after telling undercover reporters posing as constituents that he had “declared war” on media mogul Rupert Murdoch.

Mr Hunt sent a memo to Number 10 while Mr Cable was in charge, warning that he risked putting the Government on “the wrong side” of media policy.

“I looked carefully at what Jeremy Hunt had said publicly,” Mr Cameron said.

“I took the advice of the Cabinet Secretary, who took legal advice about it, and what he said publicly was more effusive, more powerful than anything he'd said privately, and on that basis I gave him the job.”

He added: “He ran it very well and, I think, reached the right conclusions.”

Mr Cameron said Mr Hunt was “the right person” to remain in charge of making a success of the London 2012 Olympics but sidestepped the question of whether he would remain in post after that.

Asked if Mr Hunt was safe in his job for at least the rest of the year, Mr Cameron said: “He's got a very important job to do.”

Labour is to use its opposition day debate on Wednesday June 13 to demand that an inquiry into Mr Hunt's actions is launched by Sir Alex Allan, the Prime Minister's adviser on the ministerial code.

Senior Conservative Bernard Jenkin has also entered the row by renewing his calls for Sir Alex to be given the power to stage inquiries without the Prime Minister's permission.

Mr Jenkin chairs the Public Administration Select Committee (PASC) which is preparing to “consider the matter again” after recess, he warned.

Labour believes Mr Hunt misled Parliament twice about his role in the bid for BSkyB and must also take responsibility for the actions of his special adviser Adam Smith who was forced to quit when a slew of damaging emails were released showing close contact with News Corporation lobbyist Fred Michel.

In a move that puts further pressure on Mr Cameron to call in Sir Alex, the Liberal Democrats indicated that their MPs may be free to vote with Labour.

"No decision has been taken about the Opposition Day motion," a spokesman said about any whipping operation as some of the party's MPs said they believed there should be a probe.

"It is a matter for the Prime Minister to decide how to handle issues of discipline concerning Conservative ministers," the spokesman added.

MP Adrian Sanders told The Observer: "The public will accept the verdict from the person who is supposed to investigate these issues far more readily than it will the verdict of the Prime Minister. What is the point of having an adviser on the ministerial code if you never use him?"

Lorely Burt said: "I thought he (Mr Hunt) should have referred himself, quite honestly, but he lost that opportunity."

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