Media boss Lachlan Murdoch has launched defamation proceedings in the Federal Court against the company which owns news website Crikey.

Mr Murdoch's lawyers filed a statement of claim on Tuesday afternoon, against Private Media, over an article linking his family to the January 6 insurrection in the US.

The analysis article, written in June by political editor Bernard Keane, named "the Murdochs" as "unindicted co-conspirators" in the deadly attack on Washington's Capitol carried out by former president Donald Trump's supporters.

It comes after Crikey's editor and publisher publicly challenged Mr Murdoch to sue the company this week.

It also published a series of legal letters sent to Crikey by the News Corp and Fox chairman's lawyers.

On Tuesday night, Crikey's editor Peter Fray said the publisher wanted its day in court.

"We invited Lachlan Murdoch to sue us and now he has," he said. "And we say bring it on.

"We stand by our story because we believe we are dealing with a matter of press freedom and public interest."

Mr Fray said it he believed it was "absurd" to prevent media in Australia discussing events of the January 6 riots in a similar way to how they are reported on in the US.

Mr Murdoch's lawyer, John Churchill, was contacted for comment.

In an article published on Monday, Private Media chairman Erich Beecher claimed Mr Keane's article did not directly reference Lachlan Murdoch.

Mr Beecher also claimed the legal threats represented an "abuse of media power in Australia".

"The headline - "Trump is a confirmed unhinged traitor. And Murdoch is his unindicted co-conspirator" - clearly refers to Rupert Murdoch, the only "Murdoch" used as shorthand by the media and the rest of the world," he wrote.

Mr Beecher wrote that the word "Murdoch" only appeared in the article twice, which focused largely on Trump's role in the state of US politics.

"The Murdochs and their slew of poisonous Fox News commentators are the unindicted co-conspirators of this continuing crisis," Mr Keane wrote in the last line of the article.

Legal letters published by Crikey this week show Mr Murdoch's lawyers were alleging the article was an "unwarranted attack on my client, without any notice and in complete disregard to the facts" and "is malicious and aggravates the harm to my client".

The case has been filed in the NSW registry of the Federal Court.

A first court date is yet to be set down.