The District of Columbia school system, faced with personnel cutbacks imposed by the city government, may be forced this fall to shorten classes for young children. The classes have grown during the last few years to include free nurseries for thousands of 4 year-olds and all-day kindergatens in most parts of the city.

D.C. School Supt. Vincent Reed said yesterday that all kindergaten and nusery classes will run only half a day for the first than the full school day that many ran last year.

After Sept. 20, some of the classes again will last a full day, but how many do so depends on enrollment and available personnel, Reed said.

Even with the possible cutback, the city's school system is the only in the area and one of very few in the country to offer free nursery classes, regardless of parent income. Last fall, they were attended by slightly more than 3,000 4 year-olds, including 1.341 who stayed at school six hours each day.

The all-day kindergatens also are highly unusual. The only other school system offering them in the metropolitan area is Montgomery County, which has them in only five schools.

Last year, 83 of the city's 129 elementary schools had all-day kindergartens. They were attended by 4,569 children. Another 3,727 children attended kindergarten for a half day, the usual practice throughout the country. Youngsters in kindergarten usually are 5 years old.

"We are trying to have as many all-day classes as we can," said Ronald Webb, an assistant to Reed, "but the superintendent believes it is better to have all the children who want to be in school for a half day, rather than have some in school all day and others not in school at all."

City children are not required by law to attend school until they are 7 years olf. Until last year, some schools et enrollment limits and turned away latecomers.

Since 1968, as birth rates have fallen and the city's population has declined, the number of students in kindergarten has dropped from a peak of about 12,000 to an expected 8,000 this fall. Meanwhile, the number of 4-year-olds in public nursery schools increased from about 400, all in the low-income Cardozo area, to 3,108 throughout the city.

The D.C. School Board has pushed for all-day kindergarten and nursery classes as a possible way of raising student achievement and to reduce the educational deficit with which many poor youngsters start regular school.

The classes also have been popular among parents for providing day care while an increasing number of mothers work during the day.

Such classes also have created additional teaching jobs although over all school enrollment declined.

This fall, however, the numbers of teaching jobs authorized in the school budget fell by 240, and kindergarten and nursery classes have lost about 15 of last year's 370 teachers.

Because of resignations and retirements, no kindergarten or nursery teachers were fired, Webb said. The number of all-day classes probably will be reduced, depending on enrollment figures, Webb said.

Webb said planning kindergarten and nursery classes is difficult because in many schools, usually in low-income areas, parents generally wait to register their children until after the term begins.

"They'll be bringing in children over the next two or three weeks and we want to take all of them," said Emma George, prinicpal at Syphax Elementary School at Half and N Street SW where most of the students are from public housing projects.

Webb said parents who plan ahead and want to make arrangements for day-care have complained about the delay in deciding whether or not their schools will have all-day classes.

"They do have a point, but we have to consider all the children," he said.