Johannesburg - An ANC councillor who allegedly attacked EFF members was denied bail by the Rustenburg Magistrate's Court on Friday.
The matter was postponed to August 22, the EFF said.
Police could not be immediately reached for further details on the matter.
"State prosecutors argued that these hooligans must not receive any bail as the safety of the anniversary preparations cannot be guaranteed," party spokesperson Mbuyiseni Ndlozi said in a statement.
The EFF is celebrating the party's two-year anniversary in Rustenburg next week Saturday.
"This court outcome is testimony to the fact that political intolerance and violence has no place in democratic South Africa. No one has any right to undermine the political freedoms of others by using violence and intimidation."
He said ANC Councillor Levoyo Tolo Maqwane allegedly led a group of party members in an attempt to declare Ward 22 in Rustenburg a no-go area for the EFF. Some EFF members' cars were allegedly damaged.