The South African Human Rights Commission (SAHRC) on Tuesday warned that it would "take action" against politicians who make statements that amount to hate speech.
This included recent statements by EFF leader Julius Malema.
"The SAHRC has on numerous occasions urged political leaders to recognise and take responsibility for the power they wield through their words," the commission said in a statement.
"At the same time, the commission remains committed to promoting and protecting the right to freedom of expression. The right to free speech is protected as a basic human right, under Section 16 of the Constitution. This right is, however, limited and hate speech is not protected under the right to freedom of expression.
"The commission is therefore deeply concerned by recent utterances attributed to Mr Julius Malema, a Member of Parliament and the leader of the EFF.
'Amount to hate speech'
"The commission is of the view that the social media utterances by Mr Malema around former [Zimbabwean] president Robert Mugabe's passing away, on a prima facie basis, amount to hate speech under Section 10 of the Promotion of Equality and Prevention of Unfair Discrimination Act (PEPUDA).
"The SAHRC condemns these racially divisive utterances, as they go against the non-racialist values upon which South Africa's constitutional democracy is founded and will therefore refer the matter to the Equality Court."
Following Mugabe's death on September 6, Malema posted a slideshow of Mugabe quotes, hashtagged #Gushungo, after Mugabe's family totem.
One of the slides read: "The only white man you can trust is a dead white man."
On Thursday, Malema banned investigative journalism units amaBhungane and Daily Maverick's Scorpio from attending party events.
Malema said this at the EFF memorial service for the former Zimbabwean president.
Speaking to party supporters, Malema said the two publications should be treated as the enemy, much like the EFF did when it banned Gupta-owned The New Age newspaper and broadcaster ANN7.
The South African Editors' Forum has confirmed its solidarity with banned journalists and its commitment to holding the EFF to account.
"Regarding the banning of certain media houses by Mr Malema and the EFF, the commission will investigate the possible violation of the right to freedom of expression under section 16(1) of the Constitution," the SAHRC statement read.
The EFF's Mbuyiseni Ndlozi told News24 that SAHRC is doing its job.
"They are free to attend to matters that are brought to their attention. We see nothing wrong."
He added that in relation to banning amaBhungane and Daily Maverick from media briefings, Ndlozi said that the EFF's right of association is reserved.
"We can choose who we stick to, hang around with. The Human Rights Commission is free to investigate.
"It's what people do when relationships break up," Ndlozi said.