The number of children enrolling in public kindergarten classes went up this year in all but one of the Washington area's major school systems, the first such growth in some districts in more than a decade.

Officials believe the increase reflects both an upturn in the birth rate and the impact of improved programs they say have drawn some students away from private schools. The higher kindergarten enrollment helped slow the rate of decline in the total student population of area schools this fall, and officials hope the new numbers signal the beginning of a more stable period for public school enrollments, which have been dwindling here and in many areas of the country for a number of years.

"We are projecting a situation of increasing enrollments in elementary schools by 1985," said Tom Snyder, a specialist at the National Center for Education Statistics. "There have been increases in nursery schools and kindergarten enrollments, and we project those figures to go up through 1990."

In the District of Columbia, 6,215 students enrolled in kindergarten this fall, up from 5,867 last year and the first increase in kindergarten enrollment since 1965, according to school system spokesman Janis Cromer.

"It seems we are turning the corner a bit in public confidence in our schools," said D.C. Schools Supt. Floretta McKenzie. "We are coming up with more students than we projected."

In Montgomery County, where kindergarten enrollment has held steady or declined each year since 1969, the number of entering students rose to 5,402 this year from 5,128 last year, according to George Fisher, director of facilities planning.

"We are having more births in the county. This year we are also offering seven more schools with all-day kindergarten classes and parents prefer that," Fisher said. "We project that we really have only one more year of decline at the elementary level."

Fairfax County schools recorded their biggest class of incoming kindergarten students since 1974: 6,916 compared to 6,485 last year, according to Dr. Roger Webb, director of facilities planning.

The only local school system to report a decline in kindergarten enrollment this fall was Arlington, where the number of entering students dropped by two, from 921 last year to 919 this year.

In Prince George's County, where officials have closed 35 schools in the past two years, kindergarten enrollment increased to 6,278 this fall compared to last year's 6,019, the lowest point in recent years. In Alexandria, 706 students entered kindergarten this fall, up from 655 last year.

In both Alexandria and Washington, officials believe that the combined effect of improved public school programs and increased private school costs have brought the public system some new students in kindergarten and in other grades who might otherwise have gone to private schools.

"We have 785 new elementary school students and increased by nearly a third the number of students coming from private schools," said Alexandria school system spokesman Mel Alba.

"Most of our gains have been with 4-, 5- and 6-year-olds," said Patricia Greer, principal of the Eaton elementary school in Washington, one of a number of D.C. schools that showed an overall increase in enrollment in all grades it serves. "In prekindergarten, we are beginning to see the children of 30-year-old parents . . . . A lot of them could have afforded private school, but they are coming here."

U.S. Census Bureau projections show an anticipated increase in the number of elementary-school-age children nationwide beginning in 1986. But the increase is not expected to match the effects of the baby boom that swelled school populations around the country in the 1960s.

"We're seeing a mini-baby boom, but nothing resembling the big upsurges of the past," said George Grier, a demographer who has done extensive studies of area population trends for the Greater Washington Research Center.

"There were predictions of a big increase in births in the early '70s, but it didn't occur," he added. "Now those women are beginning to have babies, but they are older, working women and they are going to have fewer children than women have had in the past."

This year's increase in kindergarten enrollments has helped slow the rate of decline in total student population for area schools. D.C. schools, which have seen total enrollment shrink by an average of roughly 5.6 percent annually for the last five years, this year recorded a total decline of 3.5 percent. There are now 91,105 students enrolled in all grades of the D.C. system.

Montgomery's rate of decline slowed only slightly, from a 3.3 percent decrease overall last year to a 3.2 percent decrease this year. Montgomery's total student population this year is 92,517, said Fisher.

Prince George's total student population is now 111,800, according to school system spokesman Brian Porter, a 3.8 percent decline this year compared to a 4.5 percent decrease recorded at the beginning of the last school year.

In Fairfax, the total population decreased by 1.4 percent, to 122,511 students, compared to a 1.9 percent decrease last year, said Webb. In Arlington, student popluation shrank by a total of 100 students, according to spokesman John L. Crowder, to an enrollment of 14,610. That marks a decline of less than one percent, compared to a roughly three percent drop last year.

Alexandria City schools recorded an enrollment decline of 1.7 percent, to a total student population of 10,543, Alba said, "one of the smallest membership declines we have had in the past decade."