Fox News boss Lachlan Murdoch has launched legal proceedings against Australian media outlet Crikey, accusing the site of defaming him in an opinion piece about the January 6, 2021 US Capitol riots.

The lawsuit was filed late Tuesday in Australian federal court, a day after Crikey made public a cache of legal letters sent by Murdoch's lawyers since the article's June publication and dared the media scion to sue it.

Crikey even took out an advert in The New York Times on Monday, publishing an open letter that welcomed the opportunity to "test this important issue of freedom of public interest journalism in a courtroom."

Murdoch is chief executive of media behemoth Fox Corporation and co-chairman of News Corp.

He is the eldest son of billionaire media tycoon Rupert Murdoch, owner of scores of outlets including Fox News, The Wall Street Journal and the New York Post.

Crikey's article - headlined "Trump is a confirmed unhinged traitor. And Murdoch is his unindicted co-conspirator" - did not name the younger Murdoch directly.

However, it did refer to the "Murdochs and their slew of poisonous Fox News commentators" in its final paragraph.

Murdoch's lawyers claimed in letters to Crikey that their client was defamed 22 times in the article and its social media posts.

While Crikey initially deleted the article on the day it was published as a "goodwill gesture" after Murdoch's lawyers made contact, the piece was reinstated amid the legal wrangling.

Crikey editor Peter Fray and chairman Eric Beecher said on Wednesday that the site "stands by its story."

"We look forward to defending our independent public interest journalism in court against the considerable resources of Lachlan Murdoch," they said.

"We believe that coverage of the events of January 6 at the US Capitol, and the role of Fox News in those events, is absolutely legitimate."

The story has made waves in Australia, where the Murdoch family remains a major player in the local media despite its global expansion.

Former Australian prime minister Malcolm Turnbull even weighed into the saga on Wednesday, saying he was "very surprised" by Murdoch's decision.

"I think it's hypocritical," he told radio show RN Breakfast, adding that the Murdochs were "always bleating about freedom of speech, and how the defamation laws are too harsh."