Participation in the school lunch program dropped by 3 million students last year when federal funding was cut at the request of President Reagan, according to reports compiled by the Agriculture Department. One-third of those dropped were low-income students.

In a related report, the Food Research and Action Center (FRAC), a private, nonprofit advocacy group on food programs, said yesterday that its survey of 44 states corroborated the department figures on reductions in participation, and showed that students who remained in the program ate substantially more nutritious meals -- with more milk, fruit and vegetables -- than those who were out.

The Agriculture Department, in an internal update on the food program, calculated that average monthly participation in the school lunch plan dropped from 26.2 million children in the 1980-81 school year to 23.1 million in 1981-82.

About one-third of the reduction involved low-income children.

Under the program, any child in a participating school can buy the special lunches, but only low-income children get direct subsidies on the price of the meal. The number of schools participating fell from 93,982 to 91,260.

According to the same report, participation in the school breakfast program fell 475,000, from 3.8 million to slightly more than 3.3 million, and about two-thirds of those who dropped out were low-income students.

The program changes, which knocked about $1 billion from the program, reduced federal subsidies for meals for non-poor children and tightened eligibility cutoffs for free and reduced-cost meals, were enacted at the urging of the Reagan administration in 1981 as part of its drive to cut federal spending.

In the report on its survey, FRAC said that in elementary schools, 91 percent of the children participating in the program had milk as part of their lunch, 99 percent had fruit or vegetable juice, 75 percent had a vegetable and 65 percent had fruit.

But only 50 percent of nonparticipants had milk, 8 percent had juice, 14 percent had a vegetable and 28 percent had fruit.

Nonparticipants ate more sandwiches, cake, pretzels and potato chips.

FRAC also said the reduction in participating schools resulted in part from a cut in what amounts to a special overhead and operating subsidy paid to participating schools for non-poor students.

FRAC said many schools stood to lose money on the program as a result, and therefore dropped out, making lunches unavailable to poor and non-poor alike.