Fairfax County Executive J. Hamilton Lambert has rejected an offer to join the administration of Virginia Gov.-elect Gerald L. Baliles as the cabinet officer in charge of the state's transportation and prison systems.

"I was deeply honored by his consideration," Lambert said in an interview yesterday.

The 45-year-old official said that he turned down the Richmond offer because "I believe I have significant unfinished commitments in this area I must honor."

The position of secretary of transportation and public safety, which in recent years has been embroiled in some of the most controversial problems in Virginia, carries an annual salary of $71,546.

This is almost $20,000 less than Lambert is paid as chief executive officer of the largest local government in the state.

"Baliles did have discussions with Jay Lambert, but Lambert withdrew his name from consideration for the secretariat," said Baliles' press secretary Chris Bridge.

Baliles, who has announced four of his cabinet-level appointments, is expected to name his selections this week for the two remaining cabinet jobs, Bridge said.

A Democrat, Baliles was elected Nov. 5 and will take office Jan. 11.

Lambert, 45, who began working as an assistant draftsman in the Fairfax County government after graduating from Loudoun County High School, has been head of the Fairfax government since 1980.

Northern Virginia legislators last year said Lambert and his staff were instrumental in helping them push through legislation in Richmond that changed the way the state distributes highway construction money, shifting a greater percentage to urban and surburban areas.

"We had great pride," that Lambert had been offered the job, said Fairfax Supervisor Thomas M. Davis III. He said if Lambert had accepted the position, "we'd have to scramble" to find a good replacement.