In a statement, Ndabeni-Abrahams said she would like to offer her sincere apologies for "an incident" with some members of the media.
"I wish to assure the media and South Africans at large my unreserved commitment to media freedom. I sincerely regret the incident," Ndabeni-Abrahams said.
The forum said while it noted the minister had apologised for the incident, it was concerned that she referred to her actions as an "altercation".
"Given the minister’s high profile portfolio relating in particular to the SABC, we would like to have an urgent meeting with her to discuss the matter and our concerns," Sanef said in a statement.
Sanef said it also saluted the SABC for airing the footage, showing fierce editorial independence and a shift from the recent past where freedom of expression was undermined at the public broadcaster.
The Democratic Alliance said Ndabeni-Abrahams’ actions were no different from previous ANC ministers who had sought to control the SABC through political interference.
"Her act is not a once off or a mistake, she was simply doing what the ANC has been doing for years, and were allowed to by captured SABC management and boards.
"We applaud the SABC for taking a firm stand and encourage it to report any attempts of persecution by the ANC for simply doing what is required of the SABC as an independent public broadcaster, not ANC mouthpiece," the DA said in a statement.