Lachlan Murdoch has paid $840,000 in legal costs to a small Australian publisher after he dropped a defamation lawsuit accusing the company of linking his family to the Jan. 6 Capitol riot, his lawyer said on Tuesday.

Mr. Murdoch’s lawyer, John Churchill, said in a statement that Mr. Murdoch, the chief executive of Fox Corporation, said the payment covered all of the costs that Private Media, the publisher of the news website Crikey, faced because of the libel case he had brought against the company. The amount equates to about 1.3 million in Australian dollars.

Mr. Murdoch dropped the lawsuit in April, two days after Fox News settled a separate defamation lawsuit filed in the United States by Dominion Voting Systems, an election technology company, for $787.5 million.

Mr. Churchill said in the statement on Tuesday that Mr. Murdoch remained confident that a court would have ruled in his favor, but he discontinued the suit because he did not want to “facilitate a marketing campaign designed to attract subscribers and boost their profits.”

Mr. Murdoch sued Crikey last August over an opinion column with the headline: “Trump is a confirmed unhinged traitor. And Murdoch is his unindicted co-conspirator.” The column did not specify whether it was referring to Mr. Murdoch or his father, Rupert Murdoch. The article argued that the Murdochs and Fox News commentators were culpable for the 2021 insurrection at the Capitol by pushing false claims of voter fraud in the 2020 presidential election.

The libel suit became intertwined with the Dominion case after Crikey added thousands of pages of evidence unearthed by the voting technology company. Dominion had accused Fox of defaming it by repeatedly linking it to the false voter fraud claims in multiple broadcasts.

Will Hayward, the chief executive of Private Media, wrote in an article published on Crikey that money the company had raised through crowdfunding to help pay for the legal costs — about $378,000, or about 588,000 in Australian dollars — would be donated to the Alliance for Journalists’ Freedom, an Australian nonprofit. That donation was a condition of the agreement with Mr. Murdoch.

“This money was raised from the good will of people across Australia who believe in the importance of free speech,” Mr. Hayward said. “These funds will now go to support the alliance and its team as they champion that cause across the world.”