Jacob Rees-Mogg is facing criticism after he accused a journalist of being “either a knave or a fool” over a story about the foreign secretary, Dominic Raab, the second time in recent weeks ministers have targeted individual reporters with claims of distorted coverage.

The National Union of Journalists (NUJ) said Rees-Mogg was among ministers of “acting like playground bullies”, while Labour accused the government of routinely undermining journalists.

HuffPost UK, the outlet targeted by Rees-Mogg, responded by accusing the leader of the Commons of using the legal privilege of speaking in parliament “to smear a journalist”, and demanded he produce evidence for the allegation or retract it.

HuffPost was also the outlet involved in the earlier ministerial attack, at the end of January. Then, the Treasury and equalities minister, Kemi Badenoch, used Twitter to accuse another HuffPost reporter of “looking to sow distrust by making up claims”, allegations Badenoch has never substantiated.

Rees-Mogg’s outburst came during his regular ministerial question session on Thursday morning, when the shadow leader of the Commons, Valerie Vaz, asked about a story on Tuesday by Arj Singh, HuffPost’s deputy political editor.

The story quoted a leaked extract of a video call between Raab and staff in his department in which the foreign secretary said it was possible the UK could strike trade deals with countries whose human rights records breached the European convention on human rights (ECHR).

“If we restrict it to countries with ECHR-level standards of human rights, we’re not going to do many trade deals with the growth markets of the future,” Raab said. Raab’s department said later the leaked extract had been “selectively clipped”, and that the minister’s fuller comments highlighted a more nuanced approach.

Speaking in the Commons, Rees-Mogg said Raab’s words had been “shockingly distorted by low-quality journalism”, adding: “It’s a very cheap level of journalism, it’s not a proper way to behave.”

Raab had been “absolutely clear” that rights abuses could affect trade, and that the recording was edited “unfairly, improperly, and broadly dishonestly”. Rees-Mogg added: “I think we should look at that type of poor-quality, online journalism. It’s not the sort of thing that would happen in the Times.”

At the end of the ministerial session, Vaz raised a point of order to note that HuffPost had contacted her to reject any accusations of dishonesty.

Rees-Mogg replied: “If the journalist didn’t clip it himself, he ought to have known it was clipped. He is either a knave or a fool.”

In a tweet, Jess Brammar, the editor-in-chief of HuffPost UK, said: “To use parliamentary privilege to smear a journalist – knowing you can’t be sued for defamation because you are saying it in parliament – is extremely troubling. We stand by Arj and his journalism. Produce your evidence, Jacob Rees-Mogg, or retract and set the record straight.”

Asked repeatedly in a Downing Street media briefing whether No 10 endorsed Rees-Mogg’s language, Allegra Stratton, Boris Johnson’s press secretary, declined to explicitly do so, saying: “I think we’re just saying that we regret that this particular audio was selectively clipped.”

It was, Stratton told reporters, “best practice to run as much of the context for a single sentence as possible”.

Asked if the UK might nonetheless make trade deals with countries that did not meet ECHR right standards, Stratton said: “That’s a separate issue that is being resolved elsewhere on the trade bill.”

Michelle Stanistreet, general secretary of the NUJ, noted that the government had recently brought out a new government action plan on journalists’ safety: “Yet here we have colleagues around the cabinet table acting like playground bullies, undermining the work of journalists, bringing their work into disrepute, and dishing out insults that are clearly designed to further inflame harassment and abuse online.”

Jo Stevens, Labour’s shadow culture secretary, said Rees-Mogg should retract his comments and apologise. She said: “There is sadly a pattern with this Tory government of undermining the hard work of journalists who challenge them, while claiming to support freedom of the press.”