The Fairfax County Board of Supervisors yesterday called for a smoking ban in all public schools in the county and promised to provide money for monitors to enforce the rule.

Tobacco is now forbidden all but 10 of Fairfax's 23 high schools under a school board policy that allows school principals to decide whether their students may smoke at school.

That troubled Supervisor Audrey Moore (D-Annandale), who sponsored the no-smoking resolution. "I think it's time for the school board to take the principals off the hot seat and make this a countywide policy," she said yesterday.

Her resolution, which passed with only one of the eight supervisors present abstaining, urges the school board to impose the ban countywide. Fairfax school spokesman George Hamel said he didn't know when the school board will consider the request. In the past the school board consistently has been opposed to students smoking in school, but has said that such decisions should be left up to each school, because the support of principal, teachers, parents and students is necessary to make any ban effective.

Montgomery County is the only other area jurisdiction that leaves smoking decisions up to principals. The Board of Education there approved a countywide smoking ban in November, but after considerable controversy withdrew it in May, opting instead for the school-by-school approach.

The District prohibits smoking in its schools, while Alexandria, Arlington and Prince George's allow smoking in specially designated areas.

Supervisor Moore said the key to a no-smoking policy is the use of smoking monitors, whom students call "smoking narcs," to police such places as bathrooms and lounges.

The effectiveness of the monitors has been hotly debated in Fairfax, where most school officials say it has been successful but many students disagree. The students claim that it is not uncommon to find cigarette butts and tobacco smoke in bathrooms of Reston's South Lakes High School, for instance. Smoking has been banned there since the school opened in 1978.

"You're always going to have a small minority that's going to smoke," said Moore. "But by making smoking acceptable, that minority is increased." She also argued that drug usage has dropped in schools with smoking bans.

Last year Fairfax spent about $133,000 on 14 monitors who ferreted out smokers and counseled them on the evils of tobacco. The supervisors assured the school board that if more monitors are needed to enforce a ban in the remaining 10 high schools, those positions would be funded for the 1984-85 school year.

Supervisor Joseph Alexander, the board's senior Democrat, abstained from the vote, saying he was not convinced that the county should be increasing the number of smoking monitors, when additional workers are needed in many other county programs.

Board Chairman John F. Herrity was out of the room when the board voted.

In other action, the board agreed to hold a hearing on a proposal to establish a residential permit parking zones, in which would only residents and their guests would be permitted to park in certain neighborhoods during peak commuting hours.

The policy is designed for areas such those around Metro stations that attract commuters. Under the proposal, such a parking zone would be established near the Huntington station before its scheduled December opening. Other neighborhoods could petition to have the program include their streets.

The board also voted to send a letter to Metro officials to inquire about press accounts that the Huntington opening could be delayed because of a lack of rail cars. Board members said they would be upset by any such delay, because the Huntington line is a year behind schedule already.

"We have put a lot of money in the system and we expect it to be open at a reasonable time," said Alexander.