A 51-year-old man allegedly shot his girlfriend and murdered her two daughters before killing himself in Rustenburg, North West, police said on Tuesday.

Police spokesperson Lt-Col Amanda Funani said the man forced the 45-year-old woman into his car and drove to a field.

Funani said that following an argument, the man allegedly shot the woman in the shoulder before she managed to escape. He then drove back to the woman's house, where he shot and killed her two daughters, aged 11 and 15, in their sleep.

The man fled the scene in his Nissan bakkie.

Funani said his charred remains were found inside his burnt out bakkie about 20km away from the murder scene.

The incident happened in Legkraal village near Mogwase, Rustenburg on Monday.

The woman was recovering in hospital.

Cases of murder and attempted murder had been opened.