The union said it had written to the police and the finance ministry to make resources available for this initiative.
It said teachers were faced with violence from different perpetrators, including community members, drug dealers, hired assassins and ill-disciplined pupils.
The Mercury reported on Monday that the KwaZulu-Natal Education Department was putting security measures in place, including deploying thousands of volunteers sourced from communities to schools that did not have security.
The calls for school safety come after a teacher was recently shot dead in Folweni and two school security guards in the same area were attacked, with one later dying in hospital.
A teacher was also assaulted by a pupil in Hammarsdale.
“To demonstrate the importance of school safety, the police department is hereby requested to establish a special unit dedicated to combating school-based and school-related crimes, violence and other misdemeanours,” Natu said.
“As the employer, the provincial departments have a legal obligation to ensure that all workers and pupils in public schools are safe,” it said.
Natu said it was seeking legal advice on what to do to compel the state, as an employer, to deliver on its obligation to protect all teachers and pupils.
The South African Democratic Teachers Union said violence in schools had a direct impact on educational outcomes.
“Violence dehumanises education workers and violates the fundamental right to quality public education of our pupils,” said provincial secretary Nomarashiya Caluza.
“It is our strongly considered view that school violence should be seen as a national crisis and that there must be adequate resourcing to facilitate the implementation of the National Schools Safety Framework that was developed almost a decade ago from an infrastructure and personnel point of view,” she said.
The police ministry did not respond to a request for comment.