Months of haggling between Fairfax County and Fairfax City over the cost of services the county provides the city ended abruptly yesterday when the county told the city it will cancel services unless the city pays more money for them.

"It just hit us today: we haven't had a chance to digest all the information," Fairfax City spokesman Robert Becker of the new rate schedules the county sent the city. The schedules outline what the county calls the city's fair share of the cost of such governmental services as schools, fire and resuce operations, libraries and the use of courts and sewage treatment facilities.

The city currently pays the county $8.4 million a year for these services. The two jurisdictions began renegotiating contracts for these services in March, but the talks broke off in October over disagreements concerning fire services.

Any cancellation of services would not take effect for 18 months, according to Fairfax County Attorney Frederic Lee Ruck.

"I think it is necessary for the County Board of Supervisors to insist that none of the services to the city are subsidized by the taxpayers of Fairfax County," said Board Chairman John F. Herrity. "When the county broke off negotiations over fire services. Herrity said the county "would just send the city a bill for the services it receives."

The largest contracts for more than $7 million, covers six county-operated schools in the city.

Speaking to about 150 city school teachers gathered in the Fairfax High School auditorium, County School Supt. S. John Davis said that next month he will start transfering the first of the 300 county school employees who now work in the city's schools. It will take 18 months for the complete transition, he said.

Davis said he had held open vacant positions in the county school system and county school employees working in the city will be the first to be considered for those jobs. He said more than 95 per cent of the county school employees in the city had indicated in a recent survey that they wanted to transfer to schools in the county.

There are four elementary, one intermediate and one high school serving 4,800 students in Fairfax City, according to Becker.

Wayne White, the part-time Fairfax City school superintendent, said, "Our (Fairfax City school) board is not interested in an independent school system . . . The city has made no plans . . . We may be forced to do some fast planning."