Republican John F. Herrity began his second term as Fairfax County's top elected official yesterday calling for an independent agency to monitor county spending, much like the General Accounting Office watches federal programs.

His proposal -- the only controversial note in an otherwise low-key inaugural address -- was attacked moments later by Democrat Martha V. Pennino, who is Herrity's chief rival for leadership of the nine elected county supervisors.

As the supervisors began their four-year terms, Board Chairman Herrity called for consideration of an auditor who would be independent of the county executive's office.

Herrity said his proposal was not prompted by a fear of scandal in the county's bureaucracy, but by a desire to "eliminate waste and duplication" in county spending. The county's auditing functions now are centered in its finance department, which is under the control of the county executive.

Pennino, the board's vice chairman, said she feared the proposal would hamper the board's prolonged search for a "first-class county executive." The position, which pays $61,000 a year and is the equivalent of a city manager, has been vacant for more than a year. The board was rebuffed recently when its top candidate, acting executive J. Hamilton Lambert, refused to take the job on a full-time basis.

Despite her reservations about the Herrity proposal, Pennino -- often one of the chairmen's top critics -- praised his inaugural address, saying: "I thought it was very good."

She was seconded by another influential board member, Supervisor Joseph Alexander, the senior Democratic supervisor, who said, "I thought it was a great, statesmanlike address."

Herrity proposed meetings between local and state officials to discuss highway and transportation problems in Fairfax. He deleted from his prepared remarks a reference to the controversial Springfield Bypass, the proposed cross-county road that has provked much opposition.

The chairman also said "the county must continue to look for ways to conserve and to encourage our citizens to become more conservation conscious." But again he steered away from controversy by not dealing with possible solutions.

Regarding another area of controversy -- what Fairfax teachers should be paid -- Herrity merely said: "We must work together to keep them the best paid in the Commonwealth."

Democrats hold a one-vote margin on the board that took office yesterday, a shift that will make increased scrutiny of county spending more likely and an increase in new social programs less likely. Previously, Democrats held a 6-to-3 margin on the board.

Neither of the new Republicans -- Thomas M. Davis III of the Mason District and Nancy K. Falck of the Dranesville District -- is a protege of Herrity. If the chairman wants to seize firm control of the board, officials say, he will have to persuade individual supervisors, along with some Democrats, to support his programs.

Inaugurated with Herrity were Pennino, who is serving her fourth term; Alexander, who is beginning his fifth; Audrey Moore (D-Anandale) and James M. Scott (D-Providence), both of whom are starting their third terms, and Marie B. Travesky (R-Springfield), in her second term.

The newcomers are Davis, Falck and Sandra L. Duckworth (D-Mount Vernon).