This was simply the latest case of politically-motivated interference in editorial independence at the public broadcaster, R2K spokesperson Mark Weinberg said in a statement.
"It makes a mockery of the principle of freedom of expression in the media and amongst citizens generally," he said.
SABC spokesperson Kaizer Kganyago denied the claim.
"There was no such instruction. People just interpreted things their own way. [The journalists] were told not to punt one side of the story [but] to balance it." he said.
"They spent a long time [reporting on] one side of the story without calling to get views from the other [Zuma's] side."
Weinberg said the Broadcast, Electronic, Media and Allied Workers' Union (Bemawu) had made the organisations aware of what was happening at the SABC.
He said that, according to Bemawu, some of its members at the SABC were given the instruction on Friday, when they returned from the National Union of Metalworkers of SA (Numsa) conference at which calls for Zuma's resignation were made.
"Such conduct weakens the institution, leaving media workers who are committed to editorial independence vulnerable to political intimidation," Weinberg said.
Bemawu could not be reached for comment.
Earlier this month, City Press reported that the SABC had banned broadcasts of the booing of President Jacob Zuma at the memorial service for former president Nelson Mandela.
The crowd booed when Zuma arrived at FNB Stadium, in Johannesburg, and every time his face was shown on the big screen.
This could be seen by viewers of the SABC's live broadcast of the memorial.
The newspaper said that it learnt from six independent sources, including field reporters, producers and technical crew in the SABC's news division, that an instruction was given to ban broadcasts of the booing.