Lachlan Murdoch, the chief executive of Fox Corporation, dropped his defamation suit against an Australian publisher on Thursday, two days after his company settled a blockbuster libel suit against them.

Mr. Murdoch sued Private Media, which owns the news website Crikey, in August over an opinion piece published by Crikey in June that linked the Murdoch family to the Jan. 6, 2021, riot at the U.S. Capitol.

The opinion article was headlined: “Trump is a confirmed unhinged traitor. And Murdoch is his unindicted co-conspirator.” It said the Murdochs and “poisonous” Fox News commentators were culpable for the insurrection, though it did not specify Mr. Murdoch by name.

The case had been expected to go to trial in Sydney this year. Mr. Murdoch spends most of his time in Australia, where his family lives.

In a statement on Thursday, Mr. Murdoch’s Australian lawyer, John Churchill, said Crikey had recently added to its defense case the thousands of pages of evidence that were made public in the recent lawsuit that Dominion Voting Systems, an election technology company, brought against Fox in the United States.

“Mr. Murdoch remains confident that the court would ultimately find in his favor; however, he does not wish to further enable Crikey’s use of the court to litigate a case from another jurisdiction that has already been settled and facilitate a marketing campaign designed to attract subscribers and boost their profits,” Mr. Churchill said.

Mr. Churchill said that in the Dominion case, which was settled on Tuesday for $787.5 million just as a trial was about to begin, the judge had ruled that the events of Jan. 6 were not relevant and that Dominion did not plan to argue that Fox had caused the insurrection.

“Yet this is what Crikey’s article alleged and what Crikey is attempting to argue in Australia,” Mr. Churchill said.

Crikey, which has said it stands behind the article it published, did not immediately respond to a request for comment.

Dominion had sued Fox for its role in broadcasting and promoting baseless conspiracy theories linking its voting machines to mass fraud in the 2020 U.S. presidential election. Fox’s legal team had faced a series of setbacks while trying to defend the network, including a pretrial ruling by the judge that found all of the statements about Dominion were false.

Fox and Dominion settled the case as lawyers prepared to give their opening statements before a jury. Fox did not have to issue an apology for the lies, but it said in a statement that it acknowledged “the court’s rulings finding certain claims about Dominion to be false.”

A spokesman for Mr. Murdoch declined to comment further on the resolution of the Australian defamation suit.

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