Eight people have been killed and three others injured during a mass shooting at a birthday party in Gqeberha city in South Africa's Eastern Cape Province.

Two unidentified gunmen "randomly shot at guests" who were dancing and mingling at a house party in Kwazakhele township, police say.

Vusumzi Sishuba, who was celebrating his 51st birthday, is among the dead.

No arrests have been made but police have urged the public to share any information about the shooting.

Mr Sishuba's family is "in a state of shock and disbelief," a relative told Reuters news agency.

Five men and three women, aged 20-64, have been identified as victims of Sunday night's shooting.

"These victims were killed by criminals, and we will not rest until we find out what happened and who was responsible for [this] callous and cold-blooded attack on these unsuspecting victims," said Eastern Cape Police Commissioner Nomthetheleli Lillian Mene.

The motive behind the attack is unknown.

Police Minister Bheki Cele visited the scene of the shooting on Monday and asked for patience while the investigation continued.

"We know everybody is angry and would love that we respond quickly, but we request a little bit of space so that we do the work thoroughly," he told reporters in Gqeberha, formerly known as Port Elizabeth.

South Africa has one of the highest gun crime rates in the world but random mass shootings are uncommon.

Last year, the country saw a string of shootings in separate bars which left more than 20 people dead. Those shootings are still under investigation.