Virginia will impose stricter requirements on accountants who audit local governments in the state to help prevent the embezzlement of public funds such as occurred in Fairfax City for at least six years.

Frances L. Cox, the city's treasurer for 27 years, was convicted last fall of embezzling at least $200,000 and sentenced to 10 years in prison. She is free on $75,000 pending an appeal.

City officials, who have since filed a $2.7 million civil suit against Cox and the insurance company that bonded her, estimate she actually took close to $600,000 between 1976 and 1981, much of it from tax payments and small cash fees for dog tags and other items. The suit is scheduled to be tried in October.

"Virginia has had small frauds pop up from time to time but nothing like Fairfax City . . . that put us on notice that stronger standards were needed," Norwood Jackson, state director of local government audits said yesterday.

After July 1, Virginia will require accountants who check local governments to assume greater responsibility in seeking out fraud. Under new regulations, auditors must provide "reasonable assurance" that no fraud has occurred and that frauds "will be detected as a result of the audit."

Fairfax City auditors found money missing as early as 1965 but testified at Cox's trail last summer they didn't attempt to account for it and normally consider discrepancies of 3 to 5 percent insignificant. Nearly $50,000 a year was reported missing in 1979, 1980 and 1981, but accountants listed it as "misclassified" and stated in all three years "there is no evidence of wrongdoing." Cox has blamed the problems on clerical errors.

Three firms have performed the city's audits in recent years. One, Thompson Greenspon, issued a warning to the city in 1978 that while it found no evidence of wrongdoing, "the opportunity was there," City Attorney William Roeder said yesterday.

Coopers and Lybrand, a major accounting firm, audited city books during the years when the major losses apparently occurred, Roeder said. Arthur Andersen & Co. is the city's current auditor.

The new state regulations are similar to those in other states and are the first detailed audit procedures required by Virginia for all municipalities, Jackson said.

The state also will impose the new standards on its own auditors. Under state law, localities can ask state auditors to check their books, a function state auditors used to perform in most communities, Jackson said. Today the state auditors check only about 20 jurisdictions, including Falls Church and Loudoun County.

Some accounting firms apparently are unhappy with the new regulations, claiming they will require more work and may make them liable for embezzlements they don't detect, Jackson said. He declined to identify the firms that have objected.

Stephen L. Moloney, a former Internal Revenue Service auditor elected Fairfax City treasurer in a special election last fall, said yesterday he has not seen the new regulations but endorses any tighter controls over audits.