Spokesperson for the league Troy Martens on Sunday said the magistrate should take into consideration claims in the media that there is a strong case of premeditated murder against him.
"It is with this in mind that the ANCWL urges the magistrate to heed the call of the prosecutors in this case and deny bail," said Martens.
Pistorius was arrested on Thursday after his girlfriend, Reeva Steenkamp (29), was shot dead at his home in Pretoria.
According to the City Press on Sunday: "A bloodied cricket bat is the central piece of evidence in the infolding murder investigation into Steenkamp's death. … police are investigating different scenarios involving the bat – one of which is that her boyfriend … Oscar Pistorius, used it to viciously assault her.
" … The police are also investigating two more possibilities: that Steenkamp may have used the bat in self-defence, or that Pistorius used it to break down the toilet door behind which Steenkamp was hiding from him."
The 26-year-old "Blade Runner" is currently in police custody and is expected to apply for bail at the Pretoria Magistrate's Court on Tuesday.
The league called for Pistorius to be treated like any other person accused of committing a crime of this nature.
"No special circumstances should be considered based on his celebrity status," said Martens.
Killings every eight hours
The ANCWL said that Steenkamp's death was not an isolated incident and therefore the league was extremely concerned with the high levels of femicide in the country.
Martens said the Medical Research Council of South Africa released a study indicating that a woman is killed by her intimate partner every eight hours in South Africa.
"No women should have to die at the hands of their romantic partner, but research indicates just over 50% of all women murdered are the result of intimate femicide," she said.
The league also sent their condolences to Steenkamp's family.
"Our deepest sympathies go out to the family of the bright, young woman who had the world at her feet just a week ago; but that was all taken away from her in an instant." – Sapa