Fairfax City will try to recover the thousands of dollars it lost during the administration of Frances L. Cox, the former city treasurer who was convicted this week of embezzlement, officials said yesterday.

In their first statement since Cox's conviction, the officials would say only that they believe the city's overall losses are "substantially higher" than the $160,000 loss mentioned earlier this month in an audit. The prosecutor who handled the case said repeatedly during the trial that the $200,000 in cash Cox deposited in her personal bank accounts was believed to be "the minimum" loss.

The city officials said yesterday that they were pressing an investigation into the losses that will be more exhaustive than the criminal investigation that led to Cox's conviction. "This is wider spread," said Mayor John W. Russell. "We don't know how many years we will go back because the records get hazier and hazier after about four years."

Cox, 56, city treasurer for 27 years, was convicted Thursday night of embezzling an unspecific amount of city funds during a 30-month period than ended in December 1981. Her lawyer declined yesterday to comment on the city's statement, but said that Cox is likely to appeal the conviction shortly after her scheduled Oct. 15 sentencing. The Fairfax Circuit Court jury that convicted her recommended that she be imprisoned for 10 years and she was jailed immediately.

Russell said yesterday the city was considering filing a civil suit against Cox to recover money she may have taken while treasurer. The city, he said, already has filed a claim for $150,000 with Aetna Insurance Co., which had bonded Cox.

The officials disclosed they have been conducting a dual investigation of the missing money with the commonwealth's attorney's office since possible fraud was first detected by acting city treasurer John W. Coughlan in May. "We were keeping quiet until the trial was over," Russell said. "Now we've got to start our action quickly.

City Attorney William F. Roeder Jr. said he has prepared a civil suit against Cox for any financial losses not covered by the bonding company. The City Council will be asked Sept. 27 to decide whether to file the suit and will decide then how much money to seek from her, officials said.

Deputy Commonwealth's Attorney Steven Merril said that Cox, who left office in January following her defeat, used a "very unsophisticated, very simple embezzlement scheme." He said Cox would take cash from the city's general fund and replace it with checks intended for other accounts.

That scheme created major headaches for the city last spring when citizens began receiving delinquent tax statements for bills they had already paid. "It was pretty wild around here in March and April with people calling in to complain," said one city official.

Most bookkeeping problems in the treasurer's office have since been corrected and the office is operating smoothly, Russell said. He added that city officials have prepared comprehensive guidelines to assure better accountability in the treasurer's office and said the proposals will be submitted to the council at its next meeting.