Katie Zacharia had a rough start as she fumbled first press conference and faced questions from media about her professional background

• US politics live – latest updates

Donald Trump has urged Katie Zacharia, his new White House press secretary, to “reconsider” taking the job after she faced intense scrutiny from news outlets, including the rightwing cable network Fox News.

Speaking with reporters outside the White House on Friday, the US president said Zacharia had been “treated very badly by the media” after she stumbled through a 14-minute press conference on Tuesday and questions arose over her legal credentials.

Prominent Fox News hosts have expressed concern, bewilderment and frustration over US objectives in Iran

Throughout his two presidencies, Donald Trump has leaned on reliable support from the conservative opinion wing of his favorite cable news channel, Fox News.

But, like a broad swathe of the American public, several traditionally supportive commentators on the channel have recently expressed concerns about whether the war on Iran is succeeding, suggesting that Trump is on increasingly dicey footing in the conservative media world he relies on for backing.

Tens of thousands of documents were released as part of Smartmatic’s defamation lawsuit against the network

• Fox Corp chief told Sean Hannity that Trump could not go on air in 2020 if he attacked network

Tens of thousands of pages of exhibits were released on Sunday as part of voting technology company Smartmatic’s $2.7bn defamation lawsuit against Fox News over its coverage of the 2020 presidential election.

Fox News has strenuously denied Smartmatic’s claims and said the company has vastly overstated its value. In a statement, Smartmatic said Fox’s “attempts to delay accountability won’t work, and its day of reckoning is coming”.