Treasury Secretary Donald T. Regan urged Congress yesterday to allow financial institutions to pay interest on all checking accounts, a decision that would give consumers and businesses in excess of $1 billion a year in interest.

Acting as chairman of the Depository Institutions Deregulation Committee, Regan asked the leaders of the Senate and House banking committees to repeal a 50-year-old law forbidding the payment of interest on checking accounts.

The committee of financial regulators voted in favor of the action at its last meeting on June 30 but concluded it did not have the authority to do it by regulation.

The proposal would authorize DIDC to set interest rates on all checking accounts. If the law went into effect today, the rate would be 5 1/4 percent, the current ceiling for regular NOW (negotiable order of withdrawal) accounts.

A spokesman for the American Bankers Association, which opposes the measure, said banks would incur "significant problems adjusting" to interest-bearing checking accounts. Thrift institutions, with only minuscule amounts in interest-free accounts, applauded the idea.

Banks now hold some $245 billion in checking accounts on which they pay no interest. This figure includes the accounts of households, partnerships and corporations, but excludes the holdings of domestic banks, the U.S. government and foreign countries.

A study done for DIDC by the Federal Reserve last June estimates that, in the first year, the pre-tax cost to banks of paying interest on $180 billion in business checking accounts would be between $720 million and $1.4 billion, or between 4 and 7 1/2 percent of their 1982 income before taxes.

The range is due to the uncertainty over how many commercial accounts would be upgraded to interest bearing accounts. The best estimate is about half. The reason is that banks now offer a variety of so-called free services in exchange for not paying interest on checking. These include check cashing, payroll accounting, data processing, and foreign exchange.

As many individuals have found, once banks begin to pay interest on checking, they also charge fees for services. Fed economist Fred Furlong said many large businesses might find the fees for services offsetting the interest paid. Small businesses using fewer services would benefit more from a change in the law, Furlong said.

The benefit to individuals is less clear. The Fed study originally projected paying interest to the many households who maintain traditional checking accounts could amount to between $80 million and $180 million in the first year. The estimate was predicated on the removal of all interest rate ceilings. However, in the message sent to Congress, Regan asked that the 5 1/4 percent limit be maintained on all accounts under $2,500 until all interest rate controls are removed in March 1986. Because people already can set up regular NOW accounts paying 5 1/4 percent, there is little reason to switch.

Legislation to allow payment of interest on checking was introduced first back in 1978 by House Banking Committee Chairman Fernand St Germain (D-R.I.) and again most recently as last month. The ABA once sued successfully to prevent interest on checking for government units. It is to avoid possible future litigation that the DIDC decided to hand the issue to Congress.

Regan also asked Congress to remove a requirement that DIDC meet quarterly. DIDC was created to oversee the orderly phaseout of interest ceilings by 1986, but it already has accomplished most of its work.