Northern Territory Police are calling for public assistance in relation to an aggravated assault in which a woman sustained serious head injuries in Alice Springs at the weekend.

Initial investigations indicate a 38-year-old woman was seriously physically assaulted by a 30-year-old man who is known to her, with an object, on a dirt track off Undoolya Road on Friday evening.

It is believe the pair were driving in the Alice Springs CBD area in a blue Mitsubishi 380 sedan with South Australian registration XRY394 on Friday night until Saturday at around midday.

Police attempted to stop the vehicle in two separate incidents on Saturday at which time the vehicle avoided apprehension and drove off at speed.

Police found the woman in a critical condition still inside the vehicle 90kms south of Alice Springs at a roadhouse. The male driver had fled the area and was located at a nearby property shortly after.

Police are calling for anyone who may have seen the couple driving in a blue Mitsubishi 380 sedan with South Australian registration XRY394 in the Alice Springs CBD area on Friday night and Saturday midday, or observed the pair travelling on the Stuart Highway between Alice Springs and Stuarts Well on Saturday afternoon between 12:30 and 3:30pm, to contact them on 131 444 or report it anonymously via Crime Stoppers on 1800 333 000.

The 30-year-old man is currently in custody assisting police with their inquiries.