Spokesperson Dennis Bloem said his party was not "shocked or surprised" at Zuma's statement at the commemoration of anti-apartheid hero Chris Hani in Boksburg on Monday.
"Mr Zuma is obsessed with race; he is very good in dividing our country along racial lines. His claims are nothing but a despicable red herring, which must be condemned with contempt ... Jacob Zuma is paranoid," Bloem said in a statement.
At the commemoration Zuma said there was a racism onslaught in the country which had become more direct and was no longer hidden.
He said the racism was displayed on placards during the marches.
The anti-Zuma marches last week were prompted by the President's midnight reshuffle that saw finance minister, Pravin Gordhan, and his deputy Mcebisi Jonas sacked from their jobs.
The move sparked a ratings downgrade for SA and the rand went into freefall. Marchers were – and are still – calling for Zuma to step down.
Another national march to the Union Buildings in Pretoria is planned by South Africa's opposition parties for Wednesday to demand that the president steps down.
The parties said the march was open to anyone to join. The march coincides with Zuma's 75th birthday.
"We want to remind Mr Zuma that tomorrow, Wednesday on his birthday, Cope with other opposition parties and civil society will take to the streets and march to the Union Buildings. Mr Zuma must know that the rolling mass action campaign to remove him will be intensified over the next few days and weeks," said Bloem.