Government Employees Insurance Co. yesterday said it is cutting auto insurance rates in Virginia by 5 per cent.

The rate reductions, which will save $1.9 million for Geico's Virginia customers, will go into effect when old policies come up for renewal or when new ones are written.

Reduced accident claims in Virginia made the lower premiums possible, said a Geico official.

The Virginia rate cut is the first by the company, but other could follow if claims studies show the cost of accidents is declining in other states, the spokesman said.

Geico yesterday also announced it is exercising an option to purchase $30.9 million worth of stock in subsidiary companies from American Financial Corp.

The companies are Government Employees Life Insurance Company, Criterion Insurance Co., and Government Employees Financial Corp.

Geico said it would exercise its options to buy 24.2 per cent of the outstanding stock of Gelico, 20 per cent of Crico and 20.5 per cent of Gefco from American Financial Corp., a Cincinnati based holding company.

With 135,000 policies, Geico is the second largest insurer of cars in Virginia. Nationally the company is the third largest stock company in the auto insurance business.

This month, drivers insured by State Farm Mutual, the nation's biggest car insurer, are getting dividends totaling $45 million. The dividends to be deducted from the next premium due, amount to 6.5 per cent in the District of Columbia, 5.8 per cent in Maryland and 3.8 per cent in Virginia.

Both State Farm and Geico said lower claims costs made possible the reductions in insurance costs. Geico said the size of claims had not begun to decline, but the number of claims was lower than anticipated.