The lawsuit was filed Monday by The Humane Society of the United States, Animal Protection New Mexico and residents Peter and Jean Ossorio.
The commission voted last year to allow trapping on 9 million acres of state lands, but opponents voiced concerns that the decision was based on politics rather than science.
The revised trapping rule removed the requirement to obtain permits to trap cougars on private land. It also cleared the way for using leg-hold traps and snaring on state lands.
Anna Frostic, an attorney for The Humane Society, said in a statement that trapping threatens to undermine efforts to recover species in violation of the Endangered Species Act.
“Littering New Mexico with leg-hold traps and snares will expose endangered Mexican wolves and jaguars to cruel and unnecessary suffering and death,” she said.
Lance Cherry, a spokesman for the New Mexico Game and Fish Department, called the lawsuit a distraction and said the agency will defend the trapping rule.
“The rule was crafted after nearly a yearlong process of public and scientific scrutiny, including consideration of potential impacts on endangered species,” Cherry said.
The federal case follows a similar appeal made by animal advocates in state court earlier this year.
At the time of the unanimous vote to revise the trapping rule, the Game Commission said the changes were based on sound science and research, including estimates of population densities and available habitat.
Under the rule, cougar trapping is allowed annually from November through March. Critics say many of the areas where traps will be allowed this upcoming season include habitat of the Mexican gray wolf and the jaguar.
The Mexican wolf was added to the federal endangered species list in 1976. Federal officials are working to expand the wolf release zone as part of changes made last year to the regulations on how the predators are managed.
There are close to 100 wolves in the wild in parts of Arizona and New Mexico.
Federal officials say the two Southwestern states also include habitat for the jaguar. In 2014, the U.S. Fish and Wildlife Service set aside nearly 1,200 square miles along the U.S.-Mexico border as habitat essential for the conservation of the big cats.
Federal officials acknowledged when they made the designation that no female jaguars or breeding had been documented in the U.S. in more than 50 years.