Twin Peaks horses during the roundup.
The most recent count, on July 24, found 2236 wild horses and 231 wild burros in the area.
The bureau wants to gather as many as possible, and return to the range a number which falls within the appropriate management level set for the area. Its aim is to leave or release no fewer than 450 wild horses and 72 wild burros in the area.
The bureau said the horses have desirable traits and it expected them to be in demand at auction.
It says the muster is necessary to maintain an ecological balance in the area and keep the horse population in check.
Opponents argue the use of helicopters is cruel and have challenged the need for the muster. They do not believe it is safe or appropriate to carry out the operation in the summer heat.
They argue that livestock should also be removed from the range if there are ecological concerns.