* Culture secretary denies favouring Murdoch in BSkyB bid
* Opposition want minister's conduct investigated
* PM Cameron says Leveson media inquiry must hear minister first
By Tim Castle
LONDON, April 28 (Reuters) - Prime Minister David Cameron faced growing pressure on Saturday to launch a probe into the conduct of a minister criticised over his handling of a Rupert Murdoch television takeover bid, after a judge conducting a parallel inquiry refused to intervene.
Cameron, enduring the worst crisis of his two years in power as the economy stagnates, has given his full backing to culture minister Jeremy Hunt, who was responsible for vetting media baron Murdoch's bid to take control of Britain's biggest satellite TV firm BSkyB.
Hunt, fighting for his political survival, has denied acting improperly over the ultimately abandoned $12 billion offer after emails published this week appeared to show his office had given inside information on the government's decisions to a Murdoch lobbyist.
The affair threatens to hit Cameron's poll ratings in local elections next week, following data that showed the economy was back in recession and a series of political missteps including an unpopular budget that cut taxes for the richest.
Cameron had said the BSkyB matter would be addressed when Hunt, also responsible for the 2012 Olympic Games in London this summer, appeared in the coming weeks at a separate judge-led inquiry into the media.
But that avenue was closed late on Friday when the inquiry's judge Brian Leveson refused to bring forward Hunt's appearance as a witness and an inquiry source said Leveson could not rule on whether Hunt had broken a ministerial code of conduct as that was beyond the judge's remit.
The opposition Labour party said Cameron was looking weak and evasive by not referring Hunt to a special adviser tasked with examining failures of ministerial behaviour. Only the prime minister can make such a referral.
"He must now refer this matter ... the longer the prime minister resists this, the more people will conclude he has something to hide," said Labour leader Ed Miliband.
Cameron's office said on Saturday the prime minister might eventually refer Hunt over his conduct, while insisting that Leveson's inquiry must examine him first.
"It does not make sense to cut across a judicial inquiry with a parallel process that would risk pre-empting, duplicating or contradicting it.
"Once Jeremy Hunt's evidence is made public and he is questioned, if there is anything that suggests there has been a breach of the code the prime minister would of course act," Cameron's office said.
Hunt had asked Leveson to bring forward his appearance at the inquiry to allow him to rebut claims he had improperly favoured Murdoch's News Corp over the BSkyB bid.
Conservative party deputy chairman Michael Fallon said Hunt needed the chance to defend himself at the inquiry, which released the emails sent between PR executive Frederic Michel and Hunt's political adviser Adam Smith, after hearing testimony from Murdoch's son James.
"We have only had one side of the story from Murdoch's PR man," Fallon told BBC TV.
News Corp withdrew its bid for BSkyB in July following public outrage over the disclosure that journalists from Murdoch's News of the World tabloid had hacked the phone of a murdered schoolgirl.
The ensuing phone hacking scandal prompted searching questions over the close relationship between police, politicians and Murdoch's British newspapers, leading to the establishment of Leveson's inquiry.
Hunt says he had acted with "scrupulous fairness" during the BSkyB bid and has promised to pass to the Leveson inquiry all communications between himself and his political adviser.
The adviser quit on Wednesday over the email disclosures, saying he had been acting without Hunt's authorisation in his exchanges with the Murdoch lobbyist.
But opponents say Hunt remains vulnerable as the ministerial code says ministers are also responsible for the actions of the advisers they appoint.