A citizens' committee in Fairfax County recommended yesterday that the bulging county government move its offices out of Fairfax City to a site near the intersection of Interstate Rte. 66 and Rte. 50.

At the same time, the citizens' group which was appointed by the county supervisors, said that a new county courthouse scheduled to be built by 1981 adjacent to the county's existing government offices in Fairfax City should remain at the planned site.

The citizens' group, headed by Reston lawyer Michael Horwatt, said that the county could save nearly $50 million during the next 40 years by moving the government from the 12-story Massey Building in Fairfax City to a proposed 154-acre site west of Fairfax City at Rtes. 66 and 50.

Horwatt's group estimated that it would cost the county about $110 million during the next 40 years to stay at its Fairfax City location, compared to about $60 million at th proposed site.

Most of the extra cost would go for rental of county office space in Fairfax City and construction of more parking facilities, according to the group's report. In addition, the citizens' panel estimated that the county would reap about $15 million in extra tax revenue from the businesses and offices that usually spring up around a major governmental complex, money that is now lost to Fairfax City, an independent jurisdiction.

Horwatt said the move could be accomplished by 1985. He said, however, that the "county should begin planning now for the orderly transition to a new site and construction of new facilities."

The county government has been located at roughly its present site since 1800. In recent years the country bureaucracy has outgrown its year-old glass and concrete tower and the country has had to rent more space in 15 buildings scattered throughout Fairfax City. The rentals cost county taxpayers $741,000 last year, according to Fairfax officials.

At the same time, county and city officials have engaged in a long-running feud over the amount of money the city pays to the county for various governmental services.

As a result, the supervisors authorized the study of moving the entire governmental and courthouse complex. The board is scheduled to hear a report on the issue next Tuesday night, but was not scheduled a vote. If the supervisors decide they also want to try to move the courthouse, they would have to vote before April 14 in order to put the courthouse location issue on the June primary election ballot as a county-wide referendum.