The newly elected executive of the ANC was urged on Tuesday to act decisively in tackling a number of problems in the country.
The Freedom Front Plus said if the top six failed to overcome apparent divisions in the party, the election would mark the beginning of the end for the ANC.
"The brutality of the past couple of months' leadership struggle in the ANC has left huge political wounds and illustrated the huge division within the ANC," party leader Pieter Mulder said in a statement.
On Tuesday, Zuma was elected to a second term as ANC president at the party's national conference in Mangaung. He was up against his deputy Kgalema Motlanthe for the position.
Cyril Ramaphosa was voted in as the new deputy president; a position from which Motlanthe withdrew his nomination. Gwede Mantashe was voted in as secretary general, Jessie Duarte as deputy secretary general, Baleka Mbete as national chairperson, and Zweli Mkhize as treasurer general.
Mulder said Motlanthe not being elected president meant the ANC had "in a very cruel manner... sent him into the political wilderness".
The ANC Youth League congratulated the new office bearers and called for "radical policies" from the national conference underway in Mangaung.
"The young people of South Africa are tired of promises."
The Eastern Cape ANC branch said it was happy the people it had nominated at its provincial conference had been elected to the top six.
"The focus now is to ensure that the Eastern Cape has a strong representation in the national executive committee, as additional members are being elected today."
Business Unity SA welcomed the return of some candidates to the top six, and the introduction of new faces.
"We singularly embrace the mix of continuity and introduction of new and fresh leadership, which we hope will underscore the injection of new ideas as well as the continuance of existing country programs."
The organisation called on the newly elected leaders to make speedy progress in improving investment confidence in the country, fighting corruption and helping the poor and jobless.
"The time is now to get down to work, rebuild and reclaim lost ground as a matter of urgency."