The South African president, Cyril Ramaphosa, has admitted the country is facing a national crisis of violence against women as protesters took to the streets for a third successive day.

Ramaphosa addressed the nation on Thursday evening with a plan of action to curb the scourge of gender-based violence, including a proposal to make a register of offenders public. He claimed laws would be reviewed in parliament imminently.

Women have called for the death penalty to be reinstated for perpetrators of violence against women and children and for a state of emergency to be declared.

“We are reviewing laws on domestic violence and sexual offences to prioritise the needs and interests of survivors,” Ramaphosa said.

“We are going to overhaul and modernise the national register of gender-based violence offenders provided for in the sexual offences act to ensure it is effective in combating gender-based violence.

Protesters clash with police in Cape Town. Photograph: Rodger Bosch/AFP/Getty Images

“This national register of offenders will list all the men convicted of acts of violence against women and children. I will ask parliament to consider amending the legislation to make the register public.”

Ramaphosa has also promised 11 new courts, a review on cold cases and harsher penalties for perpetrators.

“We have established 92 dedicated sexual offences courts since 2013, with a further 11 to be opened this financial year. I will propose to cabinet that all crimes against women and children should attract harsher minimum sentences,” he said.

“All gender-based violence cases that have been closed or that were not properly investigated must be reviewed.”

A national plan to curb gender-based violence will also be implemented in school programmes, workplace policies and community initiatives.

His comments are unlikely to bring comfort to protesters, however, with two women having been found dead on Friday.

Protesters hold banners outside parliament in Cape Town. Photograph: Nic Bothma/EPA

During the early hours of Friday morning, a 31-year-old woman was shot, kidnapped and dumped in a nature reserve, and later died in hospital from her injuries. The spokesman for Western Cape provincial police, Lt Col Andre Traut, confirmed the incident but said no arrests had been made.

“Circumstances surrounding a murder and an attempted murder are being investigated by police. This morning [Friday] at around 2am, a 33-year-old man was shot and wounded at his residence by unknown suspects. His 31-year-old girlfriend was kidnapped from the residence by the suspects and dropped off at the Wolfgat nature reserve with extensive injuries,” he said.

“Both victims were admitted to hospital, where the 31-year-old female succumbed to death. The motive is yet to be determined and no one has been arrested as yet.”

Meanwhile, the mutilated body of an unidentified woman was found in the middle of the street next to a primary school on Friday morning, after witnesses saw the body being dumped from a vehicle.

Demonstrations have been held for a third successive day. Photograph: Nic Bothma/EPA

“Circumstances surrounding the death of an unknown female believed to be in her 30s are being investigated after her body was discovered. According to an eyewitness report, a vehicle was seen dropping off the body next to a primary school. The motive is yet to be established and arrests are yet to be made,” Traut said.

On Wednesday evening, a woman was found murdered at a shopping centre with multiple stab wounds to her body, while on Tuesday, a 21-year-old nursing student was abducted outside a hospital and raped.

Primedia Broadcasting, one of the country’s major networks, said female employees, including those working on radio shows and news broadcasts, would not work on Friday in solidarity with the fight against gender-based violence.

The South African-born Hollywood actor Charlize Theron has spoken out against violence against women in the country. Responding to a tweet that shared a 1999 advertisement in which she starred as part of an anti-rape campaign, Theron said the justice system had failed women.

“When I made this ad in 1999 I hoped things would change. They have not. Rape and femicide are still a huge epidemics in South Africa and clearly the system has failed women. Our leaders can’t continue to turn a blind eye, as they did with this ad,” she said.

Theron also urged men to call out potential perpetrators. “To the men in my home country – please protect our women. Stand up. Speak up. Do not be bystanders. Call out your fellow man when you see him going down a dangerous path. You have the power to change this,” she said.