The Fairfax City Council said last night it believes that $600,000 disappeared from city accounts during the tenure of former treasurer Frances L. Cox -- three times previous estimates; the council voted to try to recover the money through a civil suit.

Cox, 58, was convicted last week of embezzling municipal funds following a trial at which prosecutors said she diverted license fees and real estate tax payments to herself to finance an extravagant life style and support expensive tastes in clothes.

She has been sentenced to 10 years in prison, but is free on bond pending an appeal to the Virginia Supreme Court.

After a three-hour closed session last night, the City Council voted unanimously to file a civil suit against Cox and her bonding company to try to recover any missing money.

"The City Council agreed that a fair estimate of the missing funds is about $600,000," the council said in a terse prepared statement released after the closed session. Prosecutors at Cox's trial said they had been able to discover that at least $200,000 was missing.

City officials refused to speculate on their chances of recovering the money. Aetna Insurance Company, which bonded Cox for $150,000 as treasurer, has not yet paid a claim filed by the city several weeks ago, officials said.

Prosecutors who handled the criminal case against Cox discovered last week that she transferred to her husband and son the title to property valued at $250,000 that had been in her name. The prosecutors said she signed the transfer papers in the Fairfax County Jail where she was being held pending last week's sentencing hearing. At that hearing, Cox told the judge she had only about $1,000 in her bank account.

City officials said they conducted their own investigation of the treasurer's office independently of the criminal investigation, which covered a 30-month period ending in 1981. The officials said their investigation for the civil suit involved missing funds dating from 1976.

Cox's attorney, John H. Rust Jr., declined to comment on the council's action last night.

Thefts from the treasurer's office were discovered only after Cox, who served as treasurer for 27 years lost a bid for reelection last fall.