Save SA has obtained permission – albeit through court action – to march to the Union Buildings to demand that Zuma step down following his unpopular Cabinet reshuffle a week ago in which Pravin Gordhan was sacked as finance minister.
Other protest marches are planned in different parts of the country.
"Government has noted the planned marches set to take place on Friday, 7 April 2017 and reiterates that it is a normal working day," a statement from the Government Communication and Information System (GCIS) said late on Thursday.
GCIS warned that "those who are planning to participate in marches must do so within the designated routes in a peaceful manner.
They should refrain from any form of intimidation and destruction of property.
"Marchers should avoid making inflammatory statements or provocative actions that could incite violence. Conveners of the march should together with their marshals cooperate with the law enforcement agencies who will be deployed to serve and protect all citizens and property."
The GCIS also said the planned march and delivery of a memoranda to the Union Buildings, which is a national key point requires that prior written permission is obtained from the Presidency in accordance with the Regulation of Gatherings Act, 1993.
"Government wishes to confirm that no such request was received by the Director General in the Presidency."