Citing a dramatic increase in the number of working parents in Fairfax County over the past seven years, a county advisory panel this week urged greater government involvement in regulating and supporting private day care facilities.

According to a report by the Child Care Advisory Council, 54 percent of all county children younger than age 12 live in households where all adults are working, an increase of 46 percent over findings recorded in 1974. Nationally, 46.9 percent of children younger than 13 come from families in which both parents work.

The report also noted that 50 percent of county children under the age of two have mothers who work outside the home, while 57 percent of all elementary school-age children have working mothers.

Council chairman Jane Angrist, calling the growth in day care demands "staggering," asked the supervisors to earmark funds for licensing the county's 84 private preschool child care centers and providing them with the assistance of mental health professionals.

"If private day care it to meet the ever-increasing needs of the county's working families, the county will need to be an active partner in marshalling county, community and business resources toward that effort," the report said.

But several supervisors, while agreeing with the need to study the report, expressed strong doubts that the county could afford to increase funding for social programs at a time when the Reagan administration budget-cutters are slashing federal allocations to local jurisdictions. They also voiced worries that increased government involvement in day care could ultimately raise costs to parents and pose unfair government interference in private industry.

"Somebody has to look out for the consumers here," said Republican Board Chairman John F. Herrity, who estimated that implementation of the panel's recommendations could cost county taxpayers up to $300,000 a year. "When you over regulate, you're increasing the cost to the taxpayer and the consumer."

Included in the committee's report were recommendations that:

The county develop a voluntary accreditation system for day care centers to assure the quality of local facilities.

The county provide consulting services of a mental health professional to assist day care centers in dealing with behavioral and emotional problems of children in their care.

The county set educational standards for day care center employes.

All 84 private day care centers in the county are licensed by the state, and also must comply with local health, fire and zoning requirements. But Angrist argued that the state licensing requirements represents only a bare minimum, and are not adequate to ensure that a child receives proper care.

For example, she said, the Commonwealth specifies that a day care director have completed only 15 semester hours of college work, and sets no educational standard for day care aides. By contrast, the council report urged that the county require directors and aides to meet stiff educational requirements.

The council recommendations were challenged in a minority report by council member Elizabeth Ruppert, who argued that implementation of the council's ideas would foster expansion of government bureaucracy and duplication of county services, and ultimately could suppress private initiative in child care.

Angrist rejected Ruppert's charges and denied that the council was trying to edge out privately run centers.

"The council feels strongly that day care should remain in the private sector," she said.

Presently, the county runs 25 "extended day" facilities for elementary school aged children, allowing children to stay at school after the close of classes. It also furnishes training sessions for private day care providers.