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Inquiry lawyer Robert Jay pressed again.

The rumors were “untrue,” Mr. Murdoch finally said.

Speculation that Mr. Murdoch was seeking to inflict political pain on Mr. Cameron’s Conservatives mounted Tuesday when his son James gave damning testimony about British Olympics czar Jeremy Hunt. The younger Mr. Murdoch released documents that suggested that Mr. Hunt, a Conservative minister, secretly had smoothed the way for News Corp.’s proposed takeover of British Sky Broadcasting Group PLC, a lucrative satellite broadcaster.

Mr. Hunt’s special adviser, Adam Smith, resigned Wednesday, saying he had created a perception in his emails that News Corp. had “too close a relationship” with Mr. Hunt’s Department for Culture, Media and Sport. Mr. Smith said he had acted without Mr. Hunt’s authorization.

The rumors of revenge also have been fed by Mr. Murdoch‘s messages posted to Twitter, in particular one that attacked “old toffs and right wingers who still want last century’s status quo” — a transparent dig at Britain’s Conservative Party.

Mr. Murdoch, however, said he was criticizing extremists on both sides of the U.K.’s political spectrum.

“Don’t take my tweets too seriously,” Mr. Murdoch told Mr. Jay, sending a ripple of laughter across the inquiry room at London’s Royal Courts of Justice.

Mr. Hunt, the most senior government official dedicated to the 2012 London Olympics, has denied behaving improperly. On Wednesday he promised that he would make a “very, very determined effort to show that I behaved with total integrity.”

Speaking ahead of Mr. Murdoch’s testimony, the judge leading the inquiry appealed for people not to make assumptions about what Mr. Hunt was up to.

“It is very important to hear every side of the story before drawing conclusions,” Lord Justice Leveson warned.