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.
But the Australian Broadcasting Corporation said it had started and a public health and safety warning had been issued telling people to steer clear of an area about 300 kilometres (186 miles) southwest of Alice Springs.
The animals will be shot from helicopters under a government-funded scheme expected to last until mid June.
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.