As if Interior Secretary James G. Watt didn't have enough problems on his plate, a small band of Paiute Indians is now upset that his department won't allow them to open a brothel on their Nevada reservation.

Pauite leaders, claiming that Reagan administration budget cuts have forced them to turn to the world's oldest profession for survival, have filed suit against the Interior Department in U.S. District Court in Nevada.

"We needed a quick, income-producing business," said Jim Toner, business manager for the Moapa Band of Paiute Indians.

Las Vegas attorney Earl Monsey, who is representing the tribe, said, "The reservation is very poor. They grow a little hay. They had some greenhouses to grow tomatoes and cucumbers, but it has not been a success . . . . The government grants kept them alive. But when the world got Reaganized, those grants dried up."

Toner said that under the Reagan administration federal assistance to the tribe has dwindled from about $1 million per year to only $200,000. Unemployment on the reservation is at about 40 percent.

The 71,000-acre reservation, which is home to 315 members of the tribe, is located less than an hour from Las Vegas, and a house of prostitution seemed to be a certain source of revenue.

Under Las Vegas law, houses of prostitution are allowed under certain conditions, and in March, 1982, the tribe decided that it would open one on one of the most distant corners of the reservation, about 25 miles from downtown Las Vegas.

According to Monsey, the Paiutes "entered into a lease agreement with a brothel owner of good repute--a man who operates brothels legally."

Under the plan, the tribe would earn money from the lease as well as a quarterly $50 registration fee from each prostitute and an annual $50 registration fee from other employes. Tribal officials say that they expected both the prostitutes and the customers to come predominantly from off the reservation.

The Indians said the operation would have been heavily regulated--from the cleanliness of the sheets to the limit of three red lights (no more than 200 watts each) to be allowed in front of the establishment.

The Reagan administration has been outspoken in its support for free enterprise on Indian reservations, and the plan for the house of prostitution was initially approved in June, 1982, by a state office of Interior's Bureau of Indian Affairs.

But by August, 1982, James Stevens, head of the BIA's regional office, vetoed the idea. His decision was reaffirmed at headquarters last March by Kenneth L. Smith, assistant secretary for Indian affairs.

"Economic development of Indian reservations is a primary goal of this administration and federal policy in general," Stevens said in his ruling. "However, commerce generated by prostitution is not the kind of economic development envisioned by federal policy."

Interior has argued that, under Nevada law, organized houses of prostitution are outlawed in counties with populations of more than 250,000, and the Moapa Paiute reservation is in such a county.

But Monsey contends that the law does not apply on the reservation. To back that up that, he points to previous federal court decisions that while criminal laws apply to Indian reservations regulatory laws do not. Under those rulings, Indian reservations have been allowed to operate money-making bingo operations that would not be allowed under local laws.

The Justice Department, which is representing Interior in the case, has not filed an answer to the Indians' complaint. Vince Lovett, an Interior spokesman, said that his department cannot comment on the matter since it is being litigated.