RENO, Nev. — Animal rights activists and ranchers are clashing over a federal proposal to euthanize wild horses as a way to deal with their surplus numbers.

Horse advocates will mount a campaign against the proposal announced late last month by the U.S. Bureau of Land Management, a deputy director of government and legal affairs for the Animal Welfare Institute based in Washington, D.C., Chris Heyde, said.

Federal officials said they’re faced with tough choices because wild horses have overpopulated public lands in the West and they no longer can afford to care for the number of animals that have been rounded up.

But Mr. Heyde maintained the agency is seeking a “magic bullet” for budget problems caused after it began rounding up the mustangs at an unprecedented rate in recent years. He said the roundups left too many horses for the public to adopt, requiring the agency to contract for more private long-term holding facilities.

The proposal “is killing pure and simple to balance the books for an agency whose reckless management has caused immeasurable harm to a national treasure at considerable cost to the American taxpayer,” Mr. Heyde said.

Ron Cerri, of the Rebel Creek Ranch in Orovada and president-elect of the Nevada Cattlemen’s Association, said ranchers would prefer horses be adopted but euthanasia may be necessary to keep their numbers down.

“Unfortunately, it’s something they’ll have to consider,” Mr. Cerri said. “I don’t know of another solution.”

Mr. Cerri criticized the federal agency’s proposal to stop roundups of wild horses to save money. Ranchers view mustangs as competition for forage on the range.

“That would be really unfortunate,” he said. “We’re starting to get close to what’s called ‘appropriate management levels’ of wild horses on the range. If we stop the roundups, that number will blow up again.”

There are an estimated 33,000 wild horses in 10 Western states. About half of those are in Nevada.

The agency has set a target appropriate management level of horses at 27,000. About another 30,000 horses are in holding facilities, where most are made available for adoption.

Last year about $22 million of the entire horse program’s $39 million budget was spent on holding horses in agency pens. Next year the costs are projected to grow to $26 million with an overall budget that is being trimmed to $37 million.

The president and co-founder of the Let ‘Em Run Foundation horse advocacy group, Lacy Dalton, urged the agency to consider alternative solutions. They include efforts to step up birth control and legislation to provide tax breaks to large landowners willing to let horses roam on their property, she said.

The Bureau of Land Management’s announcement marked the first time the agency publicly has discussed the possibility of putting surplus animals to death.