The bodies of the four siblings, aged between four and 12 were found on Sunday.
"It is extremely abhorring that these children were not only murdered but also had some of their body parts removed. The mutilated bodies of the Mbhele children, a four-year-old Lwandle, Siphindile, seven, Lwandile, 10, and Bandile, 12, were found with multiple stab wounds.
The children were bounded with ropes before being hacked and stabbed to death," ANCKZN said in a statement.
"The ears of the three children were severed. We are calling on the community of Ngcukeni area in KwaNzimakwe village to work closely with the law enforcement agencies in arresting the perpetrator. This strange behavior of murdering children undermines the future of our country and needs to be confronted by all sectors of society."
The ANC called on all sectors of society to stand together to " defeat this strange and painful tendency" which undermine the building a caring nation, the party said.
The KwaNzimakwe community should remain calm during this difficult time and allow police to conduct investigation to unearth what happened and why children were murdered, the party said.
"The ANC conveys its deepest condolences to the Mbhele family, relatives and friends of the affected family."
Meanwhile, the ANC Women's League (ANCWL) called on its supporters, members and society at large to work with law enforcement agencies to bring the perpetrators to book.
"The lives of children must be protected by all sectors in society. The ANCWL sends deepest condolences to the family and through its local structures the ANCWL will work with members of the community and offer the necessary support to the Mbhele family during this difficult time," ANCWL secretary general Meokgo Matuba said in a statement.
Earlier, KwaZulu-Natal's Community Safety MEC Mxolisi Kaunda called for the sternest punishment for whoever was responsible for the killing the Mbhele siblings.
Kaunda said the bodies were discovered by members of the public.
"Police reported that when they arrived at the scene, they found the deceased bodies with multiple stab wounds and they had their left ears chopped off. The siblings stayed with their mother who was not at home when the incident occurred."
Police were questioning a person who was found sleeping in the home with the deceased.
"As government, we condemn the brutal murder of the four innocent children," Kaunda said.
"We call upon members of the police to thoroughly investigate this case and ensure that whoever is responsible for this dastardly deed is removed from society and locked away for a very long time. We cannot allow such brutal acts of criminality to go unpunished."
Kaunda sent his condolences to the Mbhele family.
African News Agency