Downing Street has declined to offer evidence for Jacob Rees-Mogg’s claim that a journalist was “either a knave or a fool” and deliberately distorted comments by another minister, but is standing by the allegation.

While Boris Johnson’s spokesperson said Rees-Mogg’s words were “not comments that the PM would have made”, the decision to stand by the leader of the Commons risks escalating a furious row with the media.

Rees-Mogg’s comment in the House of Commons on Thursday prompted condemnation from the National Union of Journalists (NUJ), and a demand for retraction and an apology from HuffPost UK, the website concerned.

The No 10 spokesperson declined to criticise Rees-Mogg or say that Johnson had reprimanded him, insisting that quotes by Dominic Raab, reported by HuffPost this week, “had been selectively clipped, which distorted the foreign secretary’s comments”.

The story, by Arj Singh, HuffPost’s deputy political editor, quoted a leaked extract of a video call between Raab and staff in which Raab said it was possible the UK could strike trade deals with countries whose human rights records breached the European convention on human rights (ECHR).

Asked about the story, Rees-Mogg had said the recording was edited “unfairly, improperly, and broadly dishonestly”, and condemned what he called “a very cheap level of journalism”. Challenged by Labour, Rees-Mogg said Singh “is either a knave or a fool”.

HuffPost has rejected the claim, saying Rees-Mogg used the legal privilege of speaking in parliament to launch an unwarranted attack. The NUJ accused the government of “acting like playground bullies”.

Asked about the criticisms, Johnson’s spokesperson declined to engage with them. “The PM is a staunch believer in the value of the free press and the important role journalists play in our democracy,” he said. “These are not comments that the PM would’ve made. These comments were made by Jacob Rees-Mogg and I’m confident that he can explain their intended meaning.”

The spokesperson was asked several times what evidence No 10 had to back up the claim that the story deliberately and dishonestly edited Raab’s words to change their meaning. The spokesperson did not offer any, instead merely repeating the claim.

He added that a fuller version of the audio from Raab’s speech had been provided by Downing Street. While these comments show Raab giving extra context about the role of human rights in deciding policy, they do not contradict the key point of the story, that the UK could potentially seek to trade with countries whose rights records beach the ECHR.

Asked on Thursday whether such trade deals could happen, Johnson’s press secretary, Allegra Stratton, did not deny it, saying this was “a separate issue that is being resolved elsewhere”.