In Defense of Animals, a California-based non-profit group, has taken the government to court over the practice, and a federal court is expected to rule May 26, The Arizona Republic reported Monday.
Government officials say there are too many horses for the land to sustain, making the roundups -- the government prefers the term "gathers" -- necessary. The number of wild horses and burros has swelled from about 25,000 in 1971 to about 69,000, the newspaper reported.
The wild horses compete with elk, bighorn sheep and beef cattle for food and water and damage streams and wildlife habitat, government officials say.
Sen. Mary Landrieu, D-La., has challenged Interior Secretary Ken Salazar to find a better way to manage the horses.
"I would think that watching a herd of wild horses run free in the West is one of those things we don't ever want to shut out to our children," Landrieu said. "In my view, we're on the verge of a disaster policy if we don't work hard to change that."