The General Services Administration yesterday rejected most of the bids in the first auction of the government's surplus silver, saying the bids were too far below the market price of the metal.

More than 1.25 million ounces of silver were offered for sale but only 160,000 ounces were sold, at an average price of $9.38 an ounce.

The bids accepted by the government averaged about 25 cents an ounce less than the $9.625 closing price for silver on the Commodity Exchange Inc. in New York.

Some wishful-thinking bargain hunters offered as little as $1.80 an ounce for the government silver, and several major metal dealers bid heavily in the $9 to $9.25 range.

"I think there was a lot of posturing in our first go-round -- a lot of posturing and a lot of bargain hunting," said Roy Markon, commissioner of the Federal Property Resources Service, the GSA agency that conducted the sale. "I think the system will purify itself as the sales continue," he added.

Yesterday's sealed-bid sale was the first of a year-long series of weekly sales that are meant to dispose of 46.5 million ounces of the metal, roughly one-third of the 139.5 million ounces the government had stockpiled for war-time emergencies.

The General Accounting Office has been urging sale of the silver for years, saying there is no need for the government to stockpile silver because vast quantities of it are in the hands of private citizens.

But until now the sale had been blocked by political opposition coming largely from silver mining interests. The Reagan administration steamrollered objections to the sale by promising the cash raised by selling silver would be used to buy sorely needed strategic metals.

Just before yesterday's sale, Idaho Gov. John Evans and a group of other politicians from the United States' chief silver-mining state made a last-minute plea for a postponement, claiming the sale would have a "disastrous effect" on the mining industry.

GSA's decision to reject most of yesterday's bids as too low served to calm complaints that the government might depress silver prices by dumping its surplus on the market. By selling only a fraction of the silver offered for sale, GSA left unanswered the question of how a weekly sale of one million ounces will affect silver prices.

Silver prices on the Comex jumped sharply higher after GSA officials opened the bids at 11 a.m., disclosing that 25 buyers had made bids. By the time GSA announced its decision to reject most of the bids, Comex trading had ended.

Bids for the surplus silver were expected to come in below Comex market prices because of restrictions placed on the sale by GSA and doubts about the purity of the government silver, said Walter Frankland, head of the Silver Users Association, a Washington trade group.

The successful bids at yesterday's sale came from two buyers, Mocotta Metals, a big New York gold and silver dealer, and Republic National Bank of New York.