Ziyaad Douglas, Gallo Images
The EFF has given President Cyril Ramaphosa until Friday to answer a call to allow political gatherings.
The party says the Level 3 ban on political gatherings is an "unjustified limitation" on Constitutional rights.
The EFF previously advocated against the relaxation of lockdown measures.
The EFF has set Friday as the deadline for the Presidency to respond to its demand to allow political gatherings.
It threatened Ramaphosa with litigation, if he did not heed the party's call.
A letter, dated 22 February, from the party's legal representation, Ian Levitt Attorneys, addressed to the Presidency states that the "political space, including physically attending political gatherings, municipal council sittings, offices of the legislature, as well as Parliament and the National Assembly", is currently prohibited by lockdown Level 3 regulations.