The Humane Society of the United States yesterday asked a federal court here to order government officials to enforce a law prohibiting dog fighting, including fights allegedly occurring in Southeast Washington warehouses.

Charging that dog fighting is one of the "most overtly barbaric phenomena in American society today," the society contends in its lawsuit that during the last three years it has provided federal authorities with advance information on 10 upcoming fights, including their date, time and place and sometimes the name of the promoters.

But the society charged that virtually no enforcement action has been taken.

In a report to the FBI last April, the society listed an Arlington man as a key member of the dog fighting industry and one who played a central role in arranging the fights in Washington. The man was not identified in the report.

The lawsuit, which names the Agriculture and Justice departments as defendants, was filed in U.S. District Court along with the report to the FBI.

The lawsuit said that in a typical dog fight two dogs are set upon each other, usually to fight until one or the other is killed, a grisly scene that can sometimes take more than an hour. The activity is outlawed in many states, the lawsuit said.

The federal government became involved in policing the activity with enactment in 1976 of a section of the Animal Welfare Act which prohibits interstate transportation, purchase or sale of animals for use in the fights or use of the Postal Service in connection with that activity. The secretary of Agriculture, assisted by the FBI, has the authority under the provision to investigate possible violations of the act.

In its lawsuit, the Humane Society contended that it had drawn up the April report to the FBI to assist federal authorities in developing a policy to enforce the laws that prohibit any animal fighting. The report focused on dogfights.

In the four years since the law's enactment, "the defendants' enforcement record . . . has been a history of studied inaction on the face of an abundance of information and other assistance offered and furnished" by the society, the lawsuit said. The Humane Society was joined in its suit by the International Society for the Protection of Animals and the Massachusetts Society for the Prevention of Cruelty to Animals.

The Society's report to the FBI said that dog fighting generates "millions of dollars each year," much of which is collected through illegal gambling activities, usually with minimum $20 wagers.

Cost of admission to the fights can be as high as $35 and an additional income is often collected in contest entrance fees paid by the dog owners, which can run from $250 to $1,000, and from the sale of specially designed claims, collars and other devices such as treadmills.

The case was assigned to Judge John Lewis Smith. Spokesmen for the Agriculture or Justice Departments could not be reached for comment.