Weanlings at the Rock Springs Wild Horse Facility.
One death has so far been reported. The animal died on Monday, on the second day of the operation.
The Bureau of Land Management said the horse was examined by a veterinarian with the Animal and Plant Health Inspection Service (Aphis) and found to be aged 20-plus years.
"No obvious abnormalities were discovered and the veterinarian believed the cause of death was a combination of strain and age," the bureau said.
"A necropsy was performed and the report is pending."
The bureau said the horses gathered so far appeared healthy.
It is aiming to leave about 860 horses in the herd areas, which is the appropriate management level set for the region.
About 100 mares will be treated with the fertility-control vaccine Porcine Zona Pellucida (PZP) and released back into the wilderness.
The Cloud Foundation renewed its call for a moratorium on all wild horse roundups pending development of a long-term sustainable plan for their management.
The foundation said the operation is estimated to cost at least $US3.5 million "and will leave the celebrated Adobe Town/Salt Wells Wild Horse Range - already populated with oil and gas wells - nearly devoid of mustangs.
"Some 40,000 cattle per year are allocated to graze on the 1.5 million-acre Complex as well, leaving little room for wild horses according to BLM's multiple-use interpretation," the foundation said.
"The BLM plans to continue their operation for six weeks in order to roundup 1950 horses, removing 1580 of them permanently from the Complex."
The majority of horses removed will be shipped to the Colorado State Penitentiary in Canon City which doubles as a holding facility for thousands of captured mustangs, it said.
Carol Walker, author/photographer of "Wild Hoofbeats: America's Vanishing Wild Horses", has been documenting the mustangs of Wyoming's Red Desert for seven years.
"I am witnessing the end of the wild West here as family after family of wild horses are driven into the trap, the majority of which will never return.
"These are magnificent animals who deserve to live their lives in freedom with their families. They should not be stockpiled with the more than 40,000 wild horses and burros now in government holding."
According to the National Wildlife Federation, Wyoming's Red Desert is one of the last high-desert ecosystems in North America with varied landscapes, including the sagebrush steppe.
In addition to pronghorn, mountain lion, desert elk, pygmy rabbits, greater sage grouse, black-footed ferrets and golden eagles, reside Wyoming's last great herd of wild horses.
The foundation said these mustangs trace back to the horses of the Spanish conquest and before that to their almost genetically identical ancestors who died out in North America some 7000 years ago.
Makendra Silverman, on site for The Cloud Foundation, said: "The noise of the chopper fills the air before you see a cloud of dust and running mustangs. I watched some of the last wild horses swept off our public lands with a backdrop of oil and gas wells - this absolutely must stop."
Bureau contractors are also currently rounding up wild horses in Colorado's North Piceance Herd Area.