A suspect wanted for the murder of a South African university student has been killed in a shootout with police.

The man had been linked to the death of Olorato Mongale, whose body was found in Johannesburg on Sunday, about two hours after she was reported missing, having gone on a date.

In the early hours of Friday morning, police officers found the main suspect hiding at a residential complex in the coastal town of Amanzimtoti, police spokesperson Athlenda Mathe said.

The suspect, who has not been named by the police, shot at the officers, who returned fire and killed him, Brigadier Mathe added.

Regional police commissioner Nhlanhla Mkhwanazi said that at the time of the suspect's death, he had 28 ID cards and a dozen mobile phones in his possession.

After hearing of the fatal shootout, Chriselda Kananda, a spokesperson for Ms Mongale's family, told South African broadcaster SABC News: "It is quite a relief for the family that justice for Olorato, before we even lay her body to rest, would have been served."

Ms Mongale's death has sparked a fierce debate about the levels of violence faced by women in South Africa.

The country has one of the highest rates of femicide and gender-based violence in the world.

In an impassioned statement, Police Minister Senzo Mchunu called Ms Mongale's killing "inhumane" and "gruesome", adding: "To all men, this is a plea - simple, urgent, and human: Please, stop killing women."

While continuing the search for two other men allegedly linked to the murder, the police took the parents of the deceased suspect into custody.

The suspect's mother is accused of enabling him to "evade arrest" by tipping him off about the police's presence at her house.

The police also said the suspect's father is the owner of a VW Polo allegedly used in Ms Mongale's murder.

The vehicle, which has been seized by the police, had traces of blood inside it, Brig Mathe said.

The suspect's parents were questioned in custody but have now been released, said commissioner Mkhwanazi.

Earlier this week, the police named the three suspects linked to the killing as Fezile Ngubane, Philangenkosi Sibongokuhle Makhanya and Bongani Mthimkhulu.

Two of them - Mr Makhanya and Mr Mthimkhulu - were last month arrested for kidnapping and robbing a woman in KwaZulu-Natal, using the same VW Polo involved in Ms Mongale's murder, police said. Both men had been freed on bail.

As part of their investigation into the killing, the police have identified a criminal gang or "syndicate" who have been targeting women in malls "for kidnapping and robbery", said police spokesperson Mathe.

"They propose them, request to take them out on a date. When they agree, that is when they plan to rob them," she added.

When Ms Mongale was last seen on Sunday, she was on a date with a man she had met a few days earlier at a shopping centre.

CCTV footage showed her leaving a location in Kew, Johannesburg, and walking towards a white VW Polo with fake licence plates.

The 30-year-old's friends said she was invited for a date by a man only identified as John, who she had met in Johannesburg, where she was studying for a postgraduate degree at Witwatersrand University.

She texted one of her friends shortly before leaving home, saying that she was excited and getting ready for her date.

But police later found her body in an open field, sparking public outrage and calls for justice.

The family spokesperson said Ms Mongale's body had been "brutally violated".

A candlelight vigil was held on Wednesday evening in Lombardy West, at the site where her body was found.

Family and friends have described her as an outspoken, bubbly woman who "lived with purpose and love", local media reported.