The Fairfax County Board of Supervisors yesterday demanded a meeting with Attorney General William French Smith to protest the weekend transfer of about 430 prisoners from the D.C. jail to District-run Lorton prison in southern Fairfax.

But the board rejected an idea voiced over the weekend by Chairman John F. Herrity to sue the District in an attempt to block, at least temporarily, any additional transfers.

Herrity said that the county attorney had informed the board in an executive session yesterday that Fairfax residents must be placed in jeopardy by the additional inmates before the county can make "a credible legal case."

"But if there is one breakout, it's courts here we come," said Supervisor Sandra L. Duckworth, who represents the area surrounding Lorton.

Herrity agreed that the county would "move quickly and promptly to institute whatever legal action is necessary" if any escapes or uprisings threatened the residents near the prison.

Herrity said later he had talked with D.C. Mayor Marion Barry, who asked him to "cool it."

"I'm not going to cool it. I don't think you guys did the right thing," Herrity said he told the mayor.

The supervisors also asked the Virginia congressional delegation to join them in their meeting with Smith, whom they want to enlist as a supporter of increased federal aid for improvements at Lorton. They also asked the delegation to seek more money for guards and security devices there.

In addition, the supervisors reiterated requests that the congressional delegation obtain federal money to build a prison for the District in Washington.

Fairfax and District officials long have feuded over Lorton. Herrity noted that the county already has sued the District twice over Lorton. The first time, a federal judge in 1976 declared the facility a public nuisance and ordered improvements. In the second suit, which was officially resolved last week, the District agreed to move a firing range to prevent stray bullets from going into a nearby subdivision.

The most recent controversy heated up Friday after D.C. jail inmates set fire to scores of mattresses to protest jail conditions. District corrections officials promptly decided to move about 430 prisoners to Lorton, several months ahead of schedule.

Last month, a federal judge threatened to hold Barry and other District officials in contempt of court if they did not take action to relieve overcrowding at the jail. The city's solution has been to expand facilities at Lorton, angering Fairfax officials who want the city to house all its prisoners within its own borders.

In other action, the Fairfax board voted unanimously to proceed with its planned lawsuit against Falls Church for $271,000 in unpaid construction costs on the courthouse and jail they share. The vote came despite a private plea last week by Falls Church Mayor Carol DeLong that the county consider continuing "friendly negotiations" between the jurisdictions.

Supervisor James M. Scott, whose Providence district borders Falls Church, said the "the only way to get any action is to file suit and try to recoup some of our losses."

"In every meeting they have refused to consider any request for negotiation. We have no other recourse," said Supervisor Nancy Falck of the Dranesville district, which also abuts Falls Church.