The media giant News Corp. had frequent and extensive contact with British politicians during its controversial bid to take over Britain’s largest pay-TV broadcaster, a panel probing media ethics heard Tuesday.

Prosecutors for the Leveson Inquiry disclosed a trove of e-mails sent by a News Corp. lobbyist to James Murdoch, News Corp.’s deputy chief operating officer, detailing regular contacts between the lobbyist and Culture Minister Jeremy Hunt or his advisers that appeared intended to assist the takeover bid for the British Sky Broadcasting Group, or BSkyB.

Murdoch testified Tuesday before the inquiry, set up by British Prime Minister David Cameron in July amid the ongoing phone-hacking scandal that has engulfed News Corp. and shaken the British establishment. As the panel turned its focus to Britain’s political elite — who have long been accused of fawning over the British media, and Murdoch media in particular — he denied wrongdoing and defended News Corp.’s acts of “legitimate advocacy.”

“Politicians seek the favor of the press at all times,” he said at one point.

After the day’s testimony, the leader of the opposition Labor Party, Ed Miliband, called on Hunt to step down, telling Sky News: “Now we know he was providing advice, guidance and privileged access to News Corporation. He was being a back channel for the Murdochs.”

In a statement, Hunt, who is also the government’s lead minister for the Olympics, said: “Now is not a time for knee-jerk reactions. We’ve heard one side of the story today, but some of the evidence reported meetings and conversations that simply didn’t happen.”

Cameron’s spokesman said the prime minister had “full confidence” in Hunt.

Hunt had been tasked with making an impartial decision on News Corp.’s takeover bid for BSkyB after Business Secretary Vince Cable was stripped of the responsibility for telling undercover newspaper reporters he had “declared war” on News Corp.’s chairman, Rupert Murdoch.

News Corp. eventually abandoned its ambition to acquire the 61 percent of BSkyB it does not already own after revelations that its now defunct British tabloid, News of the World, had illegally hacked into the voice mail of a 13-year-old murder victim.

In arguably the most riveting moments of Tuesday’s testimony, Murdoch listened as the inquiry’s lead lawyer, Robert Jay, read out loud e-mails sent to Murdoch by a News Corp. lobbyist. In one, the lobbyist wrote of Hunt, “He said we would get there in the end and he shared our objectives.” In another, he said he had information from Hunt’s office that was “absolutely illegal.”

For the first time, Murdoch also disclosed that he had discussed the BSkyB proposal with Cameron at a 2010 Christmas party at the home of Rebekah Brooks, formerly a top executive at News Corp. He said he had a “tiny side conversation” with Cameron in which he sought assurances that Cable’s successor would operate in an “appropriate and judicial” manner.

Murdoch also said he was “friendly” with George Osborne, Britain’s finance minister, and had discussed the bid with him briefly during a stay at Osborne’s country home. But repeatedly dismissed suggestions that News Corp.’s British papers offered positive coverage to politicians in exchange for political influence.

“If the insinuation is that there was any quid pro quo with editorial coverage versus commercial agenda, I can tell you categorically that’s false,” he said.

It wasn’t so long ago that James Murdoch, 39, was widely considered the de facto heir to his father’s vast media empire, whose companies include Fox Television, Fox News, the New York Post and the Wall Street Journal.

Since the hacking scandal erupted, however, his credibility and competence have been questioned. He resigned in February as executive chairman of News International, News Corp.’s British newspaper unit, whose publications include the Sun, the Times and the Sunday Times.

He also resigned as the executive chairman of BSkyB earlier this month, saying he did not want to become a “lightning rod” for attacks on the broadcaster.

Rupert Murdoch, who is also James Murdoch’s father, will appear Wednesday before the inquiry, at the Royal Courts of Justice in central London, and will also be summoned on Thursday if questioning spills over.