The members of the American Horse League have joined with the US Cattlemen's Association in asking the US House of Representatives to reject the Roaming Horses and Burros Act.
The bill would outlaw the killing of healthy animals and institute sterilisation and other fertility controls to manage the herds.
It would enhance an existing program to encourage adoption of the animals and would bar adopters from slaughtering the animals for human consumption.
Natural Resources Committee Chairman Nick Rahall said the bill will save taxpayer money while saving tens of thousands of wild horses and burros from slaughter.
The bill comes in response to reports of mismanagement of the herds since passage of a 1971 law designed to protect them.
It would also expand the area of land upon which the horses can roam.
"While this legislation may be well meaning, it will only result in further destruction to the equine population, the Public's land, and the Treasury," a statement from the American Horse League said.
The group said that it learned the Roaming Horses and Burros Act, H.R. 1018, may be brought up for a vote this week.
"The fact that this legislation seeks to restore the area occupied by wild horses and burros [donkeys] to 1971 levels and that it stresses and 'ecological balance' flies in the face of logic," according to Chase Adams, chief executive of the American Horse League.
"We all must remember that 'wild' horses and burros are not native to this country, or to the Public's Lands.
"They are a feral species in the United States and their Responsible Management is incumbent upon us as a Nation."
H.R. 1018 would tie the hands of the Government officials charged with that management and severely hinder efforts to use the Public's Lands to the fullest of their ability, the groups said.
It is the conclusion of the American Horse League, that the Act adds a layer of bureaucracy to the Federal Government at a time when the nation can least afford it.
"We have some issues with the current management of the 'wild' horse and burro populations. But, this Act only works to exacerbate an already dire situation especially in the West, where our Public Lands are facing overgrazing, leaving the species that depend on them in a state of neglect," the statement said.
"The populations of 'wild' horses and burros have been left unchecked for too long.
"Studies have shown that these populations may double every four years.
"That combined with other factors have led to overgrazing, leaving the Public's rangelands resembling a moonscape."