Both Lachlan Murdoch and online publication Crikey have been dealt a blow in court ahead of a landmark case that's set to test Australia's new defamation laws.

The Fox Corporation chief executive is suing Private Media, which owns Crikey, in the Federal Court over an analysis article, published in June, about hearings into the deadly January 2021 insurrection on the Capitol by Donald Trump supporters.

Mr Murdoch claims several lines in the article, including one which names his family as the "unindicted co-conspirators" of the insurrection at Capitol Hill, is defamatory. 

Ahead of the trial both parties filed interlocutory applications trying to strike out parts of each other's pleadings, but Justice Michael Wigney has dismissed them both. 

Mr Murdoch's legal team had tried to argue that a chunk of Crikey's public interest defences should be struck out, because they were evasive, ambiguous, and irrelevant. 

The application claimed that the public interest test should only be applied to the alleged defamatory parts of the story, not the entire article. 

But Justice Wigney said his arguments put forward by Mr Murdoch's barrister Sue Chrysanthou SC, were "rather high, wide and handsome".

"I would strongly incline to the view that ... the reference to 'defamatory matter' is a reference to the article, report or program which conveyed the defamatory imputation or imputations," Justice Wigney said.

"It is not a reference to the alleged defamatory imputations or defamatory sting.

"In this case, the question will essentially be whether Crikey, given what it knew or did not know... would reasonably have considered the publication of the article was in the public interest."

The ruling will allow Crikey to rely on a new public interest defence added to defamation laws in most states, which requires the plaintiff to prove they have suffered "serious harm", to reduce the number of costly defamation battles.

Justice Wigney also criticised some of Crikey's pleadings as "less than ideal" and "ambiguous", but still refused to strike them out.

"It is at least reasonably arguable that Mr Murdoch may effectively defeat Crikey's claim that it reasonably believed the article was in the public interest, by proving that Crikey published the article for the predominant purpose of harming Mr Murdoch," he said.

"Whether Mr Murdoch is able to prove that Crikey acted for that purpose ... is a matter to be determined at trial."

In his judgment, Justice Wigney said the publisher should consider filing an updated defence to fix some "ambiguities and deficiencies".

He said given this case would likely be the first test of new defamation laws it would be best to argue them in a full trial alongside the facts of the case.

Crikey had applied to have parts of Mr Murdoch's reply to its defence struck out, but Justice Wigney also refused that move.

The matter will return to court in November.