The Central Land Council said animals -- including horses, donkeys and camels -- were dying in their thousands due to a lack of food and water and a cull was necessary on humanitarian and environmental grounds.
They also argue that the destruction of water holes by the large animals was having an impact on native species which rely on the same drinking sources.
A council spokeswoman refused to confirm to AFP that the cull had begun due to sensitivities about it.
The animals will be shot from helicopters under a government-funded scheme expected to last until mid June.
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News of the cull this month sparked protests from horse lovers but the council insisted it was necessary, arguing that the horses, and camels, were suffering and dying and polluting waterholes.
"Nobody wants to see suffering, especially the traditional owners of the land who love the horses but are well aware of the terrible consequences of out of control populations," council director David Ross said earlier this month.
Ross said aerial culling was the most humane way of dealing with the animals given it was not possible to muster horses over thousands of square kilometres with few roads and no yards.
He said it was also not practical or satisfactory to muster and then truck the horses some 1,500 kilometres to the nearest abattoir.
Ross said he understood the protests against the cull, but said he had heartbreaking footage taken by motion sensor cameras of horses dying in terrible circumstances.