A massive influx of immigrants from Asia and Latin America has sharply increased the tuberculosis rate here and in other cities, a change so drastic it has reversed what was a steady decline in tuberculosis cases nationwide.

In addition, health workers say, cuts in health budgets and stiff registration rules have discouraged immigrants from seeking treatment for the disease, greatly increasing their chances of exposing other people.

Rose Schlichter, program director for the American Lung Association office here, said Los Angeles County will report about 2,000 new cases for 1981, a 30 percent increase over 1980. "We have not seen figures like this in two decades," she said.

"The national steady decline in tuberculosis cases has stopped," said Dr. Laurence Farer, tuberculosis control director for the Centers for Disease Control in Atlanta. He estimated 1981 cases would total more than 28,000, a slight increase over 1980 despite a steady decline in the tuberculosis rate among most sections of the American-born population. Tuberculosis rates have also shot up in other cities with large numbers of immigrants, such as San Francisco, which is said to have the highest rate in the country at the moment. In the Washington area, public health nurses in Arlington County report they monitored 84 percent more cases of tuberculosis in 1981 than 1980 because of the heavy inflow of immigrants.

About 7 percent of tuberculosis cases in the country occur among new immigrants, Farer said--a much higher percentage than their proportion of the population. "These are people coming from countries who have low living standards and poor health conditions," he said. Perhaps 6 percent of all Americans, 10 million to 15 million people, are infected with the tuberculosis bacterium. Few of those ever contract the disease, but the percentage of immigrants with the bacterium is much higher, as much as 50 percent in some surveys, Farer said.

Medical researchers have not been able to determine what precisely causes the bacterium to affect some people and not others, but Schlichter said some research suggests stress plays a part. "Here you have people coming into a totally different country, trying to adjust, and they have stress," Schlichter said.

The danger of immigrants spreading the disease has increased because of cuts in health services and fear of deportation among illegal immigrants, Schlichter and Farer said. The names of any persons applying for state assistance to pay for treatment at public health clinics in Los Angeles are sent to immigration officials, "so it scares the hell out of people who are illegal," Schlichter said. "If you're illegal, you don't come in until you're real sick."

Tuberculosis is an infection that attacks tissue throughout the body but centers in the lungs in more than 85 percent of cases and can spread easily when an infected person coughs. Early symptoms, including fatigue, weight loss and some coughing, are sometimes easy to overlook, thus increasing the risk of contaminating others. In later stages, victims may cough up blood as the disease destroys tissue. In some countries it is one of the chief causes of death.

Tuberculosis rates began to decline in the United States and other developing countries in the 1950s after several drugs for controlling the disease came into use. Farer said, however, that about 4 percent of cases in the United States still result in death, usually because the victim sought treatment too late. Los Angeles County reports about 100 tuberculosis deaths per year, Schlichter said.

While the tuberculosis rate has increased here, state and federal budget cuts have reduced facilities to treat poor people with the disease. The number of tuberculosis beds at the county's Rancho Los Amigos Hospital has dropped from 65 to 22 and the number of county health clinics has been reduced from 54 to 46, with more cuts to be proposed in January. Fees for the poor have also been raised, further discouraging immigrants with little or no income.

According to the Los Angeles County Health Department, the tuberculosis rate for blacks here fell 27.8 percent and for whites 44.1 percent from 1970 to 1980. In that same period, the tuberculosis rate for Hispanics increased 66.3 percent and 219.3 percent for Asians from countries bordering the Pacific.

A U.S. State Department spokesman said that as of the end of November, 561,000 Southeast Asian refugees had entered the United States since April, 1975. They are screened for tuberculosis, however, so they can usually be treated quickly, while the much more numerous illegal immigrants from Latin America enter the country with communicable diseases undetected. Estimates of the total number of illegal immigrants now in the United States range from 3.5 million to 6 million, a large portion of them in California.