Since the alcohol sales ban was lifted at the beginning of the Level 3 lockdown in June, there has been a surge in murders after a lull between March and May.
Police Minister Bheki Cele revealed this during a press briefing at the Jabulani Hostel in Soweto on Tuesday, the SA Government News Agency said.
Cele was in the area after six men were shot and killed on Monday evening.
Police are searching for three men believed to be linked to the crime.
Initial investigations established that the men were in a shack on the hostel property when three men, armed with "handguns and rifles", opened fire on the group from different positions, police spokesperson Captain Kay Makhubele said on Tuesday.
Makhubele said the shooting took place at around 23:00.
"Five [people] died at the scene and one in hospital; the seventh victim is still in hospital," said Makhubele.
He added that the motive for the killings was unknown.
On Wednesday, Cele implied that alcohol could have played a role in the Jabulani killings.
Speaking to Talk Radio 702 morning show host Bongani Bingwa about the shootings, Cele again said crime increased since the ban on alcohol sales was lifted. He said the men had been drinking, "which is not a reason to be killed" and that crime had increased since the Level 3 lockdown was implemented.
He said the men were originally from KwaZulu-Natal and had known one another, and added that police would investigate whether it may have been a revenge attack.
During the briefing on Monday, Cele also spoke about two women who were this week murdered in Cape Town and Johannesburg.
Naledi Phangindawo, 25, was allegedly attacked to death by a man known to her. The man has since been arrested.
Tshegofatso Pule, 28, was found hanging from a tree in Roodepoort on Monday. She went missing on Thursday. She was eight months pregnant and had been stabbed in the breast.
"Nationally, we'd sit back and complain about 30 people that have died," said Cele.
This was until last Monday when the ban on alcohol sales during the lockdown was lifted.
"Until Monday - 1 June - which is not an entirely dangerous day, for the first time since the lockdown, we got reports of 40 people killed. The next day there were 51 [murders] and there were 69 this past Sunday," Cele said.
During this period, police were averaging between 20 and 30 murder cases a day.
"That has now just gone up, including attempting murder, including the abuse of women and violence against women," he said.
Cele described the murder of the two women as brutal.
"It's an issue that we raise as police and law [enforcement] that [perpetrators] of crime are well known to the victims. By the look of things, both these ladies were killed by people known to them. I'm not confirming that. The investigations are ongoing," he said.
He emphasised that it was difficult for law enforcement officers to curb domestic violence.
This, he said, was because police could not monitor people's behaviour in their homes.
"Unfortunately, in those situations, we react. But it's a question, we agree, we need to take up. We [need] to work very closely with all other structures and monitor closely gender-based violence, as [cases] can be brutal as we have seen with the two ladies," Cele said.
He pleaded with men, communities and families to report suspected abusive relationships. He said this would ensure the police were proactive in responding in their action.
News24 earlier reported that trauma cases at two Cape Town hospitals had spiked substantially since the easing of lockdown regulations.
The Western Cape Department of Health confirmed to News24 that at least two hospitals already witnessed significant increases in admissions and at one of them, the majority of cases was alcohol-related trauma.