With pressure mounting, the Forest Service hit pause. Last month, Neil Bosworth, the Tonto National Forest supervisor, suspended any planned roundups for four months.

“We have explored, and continue to explore, alternatives to address the horses,” the Forest Service said in a follow-up statement. The statement highlighted the service’s discussions with cattle owners, American Indians, state groups and horse advocates to “seek a collaborative solution with the input of the public and interested parties.”

It is still not clear what that means for the herd.

In an interview, Simone Netherlands, the president of the Salt River Wild Horse Management Group, an advocacy organization active in the battle, said, “We still have a long way ahead to agree on a humane plan for the horses.”

The horses that roam along the Salt River in Tonto National Forest, as well as in the neighboring Salt River Pima-Maricopa Indian Community and Fort McDowell Yavapai Nation, have no owner, or at least none who has stepped forward since news of the plans for their removal.

Fans and protectors call them “wild horses,” which is not legally accurate, according to federal rules.

In 1971, Congress passed the Wild Free-Roaming Horses and Burros Act, which set aside 200 areas within public lands in the Western United States where certain horses and burros could live without being harmed, harassed or removed by anyone other than the agency in charge of them, the Bureau of Land Management.