Elephant populations have been increasing in some southern African countries. Photo: AFP

The attack occurred on Saturday at Kafue National Park in the west of the country.

In a video circulating online the large elephant could be seen flipping the car carrying six people over several times.

Keith Vincent, CEO of the safari group, said the vehicle was "blocked" by the terrain and couldn't move out.

The 80-year-old woman, who has not been named, died of her injuries. Officials said her remains will be repatriated to the US in the coming days.

Four other guests sustained minor injuries and are receiving trauma counselling. One woman was taken to a hospital in South Africa for treatment.

Police and the department of national parks and wildlife are investigating the incident.

"This is a tragic and we extend our deepest condolences to the family of the guest who died," Mr Vincent said. "We are also, naturally, supporting those guests and the guide involved in this distressing incident."

Mr Vincent said the vehicle had stopped because it had become trapped by "terrain and vegetation" and couldn't manoeuvre its way out of the elephant's path.

Zambia's neighbours Zimbabwe and Botswana have raised concern about increasing elephant populations in their respective countries.

Zimbabwe has recorded deadly elephant attacks in recent years.