The EFF on Tuesday joined the UDM's bid for a Constitutional Court order that Parliament let MPs vote by secret ballot in the upcoming vote of no confidence in President Jacob Zuma.
Zuma opposed the application on Thursday, saying such a ruling would subvert the rights of the majority party in Parliament.
EFF spokesperson Mbuyiseni Ndlozi told News24 that the EFF decided to join after Zuma filed his affidavit.
"Zuma should have the decency to resolve the questions of this vote of no confidence in a fair manner," Ndlozi said.
"A moral leader must be a leader who does not oppose what people want. People should be able to vote freely, without fear of intimidation."
Ndlozi said the EFF would support the UDM with additional legal counsel.
"We want to ensure that the court sees that this is not only a one-party application, but that the opposition is united.
"We want to give people the freedom to express their vote without intimidation, which is at the core of a democratic practice."
Parties opposing the UDM's application had until 12:00 on Thursday to file an affidavit. The UDM had to file its reply by 16:00 on Wednesday.
The vote of no confidence would have been held on Tuesday. Parliament however said it would postpone it until the Constitutional Court had heard the matter.