As many as 100,000 children ages 14 and under need child care in Prince George's County, but facilities exist to handle only about 11,000 children, a county task force reported yesterday. In light of that need, the county plans to establish a day-care center for county employes and encourage other employers to do the same, a spokesman said.

The task force, appointed by County Executive Parris Glendening, found the "accelerating need" for child care in the county is due to a rapidly growing number of single-parent families and an increased number of families in which both parents work.

While the shortage of day care "is especially critical for infant and toddler care," the report said, there is also a "serious" need for care for school-age children, with more than half of the 12,000 parents who returned questionnaires expressing an interest in after-school day care.

"These problems run through the state and through the country," said Abe Lavine, staff director of the study.

The number of single-parent families with children under 18 more than doubled during the 1970s to 17,500, and a 50 percent increase is projected this decade, the report said. The number of families with children under 18 in which both parents work grew by 30 percent in the 1970s to 47,000 and is expected to increase another 17 percent by 1990.

Of about 100,000 families with children under 18 in the county, in two-thirds of these both parents work or the single parent heading the household works, the study found.

Lavine said he was "surprised by the backlog of people who need subsidized day care and people who can afford to pay but are looking for good quality places to care for their children."

The study found that the County Department of Social Services has a waiting list of about 1,000 children eligible for subsidized day care, and that the list "would be much longer but for the fact that families . . . find it pointless to even apply."

The task force recommended that the county encourage employers to set up day-care facilities at their businesses. Tim Ayers, a spokesman for Glendening, said the county is in the early stages of planning such a facility for county employes, but would not elaborate.

Other recommendations of the report included improving training for day-care providers and for Health Department workers who inspect day-care centers; expanding school programs for "latch-key" childen who return to empty homes after school; and considering easing zoning laws that limit the availability of day care.

The study also found a greater increase in reported instances of child abuse in Prince George's County than in the state as a whole, with 1,310 cases reported in the county in 1984, a 50 percent increase over 1982. The increase statewide during that period is estimated at about 33 percent.

The report also said that 15 of the 27 complaints of child abuse in Maryland day-care programs during the first nine months of 1984 came from Prince George's County.