The Democratic Alliance (DA) on Tuesday referred Ekurhuleni Mayor Mzwandile Masina to the metro's ethics committee after he warned "white people" and Save South Africa that things might get "very very rough".
He asked Save SA not to "divide our nation", in his speech at the Chris Hani memorial lecture on Monday.
"It might be very rough and we are many. This is not a threat. We are many [and] it might be very, very rough," Masina said.
"It is very important that we send a very, very strong warning that we will crush any individual who stands in the way of the project of nation building and social cohesion in South Africa."
DA Ekurhuleni leader Ghaleb Cachalia argued that Marina's statement violated the Constitution.
"This is the talk of a military strongman, not of a democratic mayor," Cachalot said in a statement.
"He used a platform yesterday at the Chris Hani Memorial Lecture, and an Ekurhuleni-branded event, to make these threats and as such he must be investigated in his official capacity."
The DA was considering laying criminal charges against him for incitement to violence and intimidation.
Ekurhuleni spokesperson Gugu Didima said the mayor's office had not received any correspondence about the matter having been referred to the ethics committee. The office would respond if it was received.