LONDON - Testifying at Britain’s long-running inquiry into media standards on Thursday, Prime Minister David Cameron rejected suggestions that he traded favored treatment for electoral support by Rupert Murdoch’s newspapers, calling talk of a conspiracy “specious’’ and “unjustified.’’

“The idea of overt deals is nonsense,’’ he said, also dismissing the idea that there had been what he called “a nod and a wink’’ covert arrangement with Murdoch in return for a decision to switch editorial support to Cameron’s Conservatives in 2009, months before a general election.

Despite the denial, British media commentators seized upon a text message, read to the inquiry by lead counsel Robert Jay, suggesting that its author, Rebekah Brooks, who was at the time the chief executive of Murdoch’s British newspaper subsidiary, believed that “professionally, we’re in this together.’’

The disclosure of the previously unpublished message was particularly embarrassing for Cameron since it echoed a slogan - “We’re all in this together’’ - in the Conservatives’ campaign for the election the following year that brought him into office. But, rather than evoking a broad social inclusiveness, as it was designed to at the time, its newest iteration will almost certainly be taken by Cameron’s critics as a sign of his intimacy with the Murdoch elite.

The exchanges went to the heart of central questions confronting the British leader after months of debate over the phone-hacking scandal that inspired the inquiry, which Cameron established last year: Was the prime minister too close to Murdoch executives and editors who have been implicated in the scandal; and, as a corollary, did the relationship reflect poor judgment, or sway policy, as the Labor opposition maintains?

“Of course I wanted to win over newspapers,’’ Cameron said, referring to his approach to the British press after he took over the leadership of the Conservative Party in 2005, five years before he became prime minister. But, he said, he did not try to win favor by offering to shape media policy in Murdoch’s favor “overtly or covertly’’ in return for favorable coverage.

Cameron took issue with testimony by his Labor predecessor, Prime Minister Gordon Brown, who had suggested that the Conservatives had made a compact with the Murdoch family to win its endorsement.

“He has cooked up an entirely specious and unjustified conspiracy theory,’’ Cameron said.

Cameron appeared confident and unruffled by the inquiry’s initial questioning. But his tone sharpened when Jay implied that the Conservatives’ media policies had been influenced by the Murdoch family. Those polices “weren’t dictated by anyone else,’’ Cameron said.

And there were moments later when the disclosures about his friendship with Brooks seemed to provoke what some British commentators depicted as some awkwardness and hesitancy.