Federal wildlife managers are using cruel, outdated and ineffectual methods of protecting livestock in Northern California by killing coyotes, wolves and other predators, conservation groups declared in a lawsuit Wednesday seeking the first government environmental analysis of such tactics in two decades.

The suit, filed in U.S. District Court in San Francisco, asks only for a judge to order the U.S. Department of Agriculture’s Wildlife Services office to take a new look at the effect of its predator-killing programs in 13 Northern California counties. But representatives of the conservation groups said their goal was to gain new protections for the predators as well as their prey.

“It’s long past time that Wildlife Services joined the 21st century and updated its practices to stop the mass extermination of animals,” said Collette Atkins, a lawyer for the Center for Biological Diversity, one of the groups that filed the suit. “Nonlethal methods for dealing with human-wildlife conflicts have been shown to work.”

Eric Molvar of Western Watersheds Project, another participant in the suit, said, “Killing native wildlife at the behest of the ranching industry is morally unconscionable and scientifically unsound.”

The Agriculture Department declined to comment on the suit.

The 13 counties stretch from Sutter, Nevada and Sierra north to Siskiyou and Modoc on the Oregon border. The suit said the agency conducted its last environmental assessment of its “wildlife damage management” program in 1997 and authorized a variety of methods to control or kill predators, including aerial gunfire, sodium cyanide bombs and leg-hold traps.

The agency issued a proposed updated assessment in May 2015, under President Barack Obama’s administration, that endorsed the same methods, and invited public comment, Atkins said.

According to the lawsuit, conservation groups asked for final action in January and for preparation of a full environmental study, and were told by officials in the new Trump administration that a decision would be forthcoming “in the next several months.”

Asked for an update Wednesday, Andre Bell, an Agriculture Department spokesman, said, “I can’t speculate on a date for completion.”

Nationwide, the suit said, Wildlife Services killed more than 2.7 million animals last year, ranging from coyotes, black bears and mountain lions to tens of thousands of beavers and prairie dogs, in its livestock-protection programs.

The agency unintentionally kills thousands of animals in “nontarget species,” the suit said, including species protected by federal or state laws, such as gray wolves and California condors.

Leg-hold traps used by the agency are “internationally recognized as inhumane” and have been banned in many countries, the suit said. It said animals sometimes chew their own limbs off trying to escape, and may die of exposure because Wildlife Services often fails to check its traps.

California voters banned the use of leg-hold traps in 1998 except when authorized by agencies to protect human health and safety.

The suit also said numerous studies since 1997 have shown that killing wolves, mountain lions, bears and other predators does not protect commercial livestock and may even increase their losses.

According to studies, Atkins said, when animal-control officers kill coyotes, the herd often responds by reproducing at a higher rate. When some mountain lions are killed, she said, others move into the territory.

By contrast, the suit said, nonlethal protective measures are more humane and effective.

The conservation groups said Marin County redirected funds in 2000 from predator killing to the use of livestock guard animals — including dogs and even llamas — along with fences, light and noise sensors, and compensation to farmers for livestock losses. Annual losses since then have declined from 5 percent to 2.2 percent, the suit said.

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @egelko