Federal banking regulators issued new rules yesterday under which small savers will be able to earn higher interest rates on their deposits starting Jan. 1.

Under the new regulations, they could earn more than 11 percent.

Savings and loans associations and mutual savings banks will be able to offer slightly higher rates than commercial banks. This is to keep mortgage money flowing into the thrift institutions, to help the ailing housing industry.

Specifically, the agencies authorized issuance of new 2-1/2-year savings certificates in denominations as small as institutions choose.In some cases, these certificates may be offered in $500 amounts. The interest rate for savings institutions will be half a percentage point below U.S. government securities with equal maturities. For commercial banks, the rate will be three-quarters of a point below the government level.

Previously, savings and loan associations and commercial banks have been allowed to offer only money-market interest rates on amounts of $10,000 or more left in a savings for six months or more.

On regular savings accounts at banks and savings and loan associations now, maximum permissibl interest rates are 5.5 percent and less.

In another step, the agencies authorized an increase of one-quarter of a percentage point in the ceiling for deposits maturing in 90 days to a year. Banks will be permitted to pay 5.75 percent while S&Ls can pay 6.

Thrift institutions are the nation's largest source of housing mortgage money but have suffered a severe profit squeeze during 1979 because of soaring interest rates.

The regulatory actions to bolster housing came amid new indications of a slowly weakening economy yesterday as the government reported a decline in industrial production last month and preliminary signs of a rise in unemployment.

At the same time, Citibank -- the nation's second-largest commerical bank -- trimmed its prime rate for top corporate borrowers to 15 percent, providing further evidence that short-term interest rates are headed lower as loan demand slackens. [See story, Page E8.]

By encouraging savers to put money into thrift institutions, the federal regulators anticipated that new mortgage money will be made available starting early in the new year at interst rates below record levels of October and November.

No minimum deposits for the high interest savings were required in the regulations issued late yesterday but banking and savings-and-loan industry officials forecast that most institutions would offer the new certificates for minimum deposits of $1,000 -- except in highly competitive markets, where the minimum may be set as low as $500.

Based on prevailing market rates this week, savings institutions would be able to offer an effective yield of 11.46 percent for the new savings certificates while banks could offer 11.18 percent. In contrast, passbook savings accounts now pay 5.5 percent at federally chartered S&L and 5.25 percent at banks.

Federal government securities will continue to have an interst-rate advantage over the new savings certificates. Rates on the new savngs certificates will change monthly and compounding of interest will be allowed.

S&L executives have been pressing regulators to give them some interest-rate advantage in the wake of popular acceptance of money market certificates that -- since last March -- have had the same rates at banks. The money market investments, which require $10,000 minimums for six-month deposits, currently offer a rate of close to 11.8 percent on an annual basis.