The furor erupted when Trade Minister Moses Kuria went on the attack against Nation Media Group (NMG), a major media house in East Africa owned by the Aga Khan.
At a public event on Sunday, Kuria threatened government officials who advertised with NMG with dismissal and asked the outlet if it was a media house "or an opposition party."
"Any government department that I see is has advertised on Nation Media (platforms), consider yourself fired," he said.
In a tweet published in Swahili, he referred to the "prostitutes at Aga Khan."
He also claimed that NMG journalists had "confessed to being coerced to write anti-government stories by their editors and management in a scheme sponsored by a former president."
NMG said the tirade followed an investigation aired on Sunday by its NTV station into an alleged scandal over an import scheme operated by a state body in Kuria's ministry.
Opposition and journalist associations have called for Kuria to be censured over his outbursts, saying he was unfit to hold public office.
Kuria's "unprovoked verbal attack... was not only undignified for a state officer of his caliber, but an assault on press freedom, a cornerstone of democracy," the Daily Nation said in an editorial published on its website Tuesday.
Opposition senator Edwin Sifuna filed a censure motion against Kuria this week, warning that an attack on one media house "often leads to attacks on press freedom as a whole."
Members of opposition leader Raila Odinga's alliance walked out of the Senate on Wednesday in protest at Kuria's appearance in the chamber and the speaker's refusal to allow them to grill him.
Kuria told reporters Wednesday: "I am not apologizing."
Media associations have reacted with fury to the comments by the minister, who had taken center stage on Monday at the signing of a major trade deal with the European Union.
The Kenya Union of Journalists (KUJ) said he was "becoming a symbol of national shame" while industry regulator the Media Council of Kenya said his remarks were a "threat to press freedom and soil Kenya's global image".
Kenya's Ethics and Anti-Corruption Commission also entered the fray, saying no public bodies should be "victimized" for engaging in lawful dealings with any organization.
The Media Owners Association of Kenya said his tirade "disqualifies him from holding public office."
President William Ruto has in the past accused the Kenyan media of being biased against him, and during the campaign for the August 2022 election he threatened to pull out of a presidential debate saying he had been subject to unfavorable coverage.
He narrowly won the bitterly contested presidential race against Odinga, who continues to protest that the election was stolen from him.