The bureau's budget for the maintenance of wild horses is under pressure, with more than 30,000 horses currently held in captivity - roughly the same number believed to be free in the rangelands.
The bureau is holding off on plans to euthanize some of the horses, but the option remains open, along with the possibility of selling horses "without limitation" - a move likely to see many thousands of horses go to slaughter.
Congressman Nick Rahall, chairman of the House Natural Resources Committee and Congressman Raul Grijalva, chairman of the National Parks, Forests and Public Lands Subcommittee, have sent a letter to James Caswell, director of the Bureau of Land Management.
"We continue to be concerned about your agency's proposal to deal with problems facing the Bureau of Land Management's Wild Horse and Burro Program by defaulting to a policy of mass euthanization of thousands of healthy horses," the chairmen said.
"As recently as November 17, the Wild Horse Advisory Board and the BLM continue to support mass euthanization, even considering options to expand sale authority in ways that will lead to the extermination of more horses. The policy is not a solution - it is a failure."
The letter follows an announcement by Madeleine Pickens who has offered to provide a permanent and safe home to horses in BLM holding facilities to ensure they are not killed.
Chris Heyde, deputy director of Government and Legal Affairs for the Animal Welfare Institute, said: "Mrs Pickens is one of the most generous and compassionate individuals I have ever known.
"Mrs Pickens is acting out of pure selflessness. She has been a long-time fighter for America's horses and her commitment to protecting these national treasures is historic."
Hyde said the American public and US Congress had to come to the rescue of America's wild horses in 1971 because they were being wiped out by the BLM. The result was the enactment of the Wild Free-Roaming Horses and Burros Act.
Thirty-seven years later, they are both coming to aid of them again from the mismanagement by the very same agency, Heyde said.
"There are many other options in dealing with wild horses on public lands and AWI will be working closely with Congress and other organisations to ensure the Agency is fixed so our horses and the public are not in this situation in a few years."