The Federal Reserve Board gave conditional approval yesterday to interstate branching for U.S. banks primarily engaged in international financial operations. A final vote is scheduled for Friday.

At the same time, the regulators of the county's Federal Reserve system banks once again deferred a decision on just what type of corporate customers will be permitted to do business with these branch banks. The board ordered its staff to devise a simpler, more liberal eligibility test than the one it proposed yesterday.

The Fed's action are intended to promote U.S. exports and enable American banks to complete effectively against branches of foreign banks in this country. Instead, the question of allowing some domestic banks to establish interstate branches has resulted in a bitter controversy between large and small banks, with the latter claiming that the big banks will gain an unfair competitive advantage.

The regulation approved yesterday authorizes Edge corporations to provide full service banking for their customers. An Edge corporation - named for the New Jersey legislator whose amendment created it in 1919 - is a bank subsidiary that handles the international financing needs of its customers. Now customers will be able to enjoy one-stop banking as the Edge corporations take care of their domestic business as well.

Furthermore, Edge corporations will be permitted to establish interstate branches, something other banks are prohibited from doing under the McFadden Act. Under current law, each new Edge corporation must be organized individually; opening branches of these bank subsidiaries will be easier and cheaper.

Most out-of-state Edge corporations are located in New York, with others in Chicago, Houston, Los Angeles, Miami and San Francisco. Large insitutions like Bank of America, Citibank and Chase Manhattan have made the most of this ability to do business nationwide under the Edge Act.

Since the regulation was proposed last February, the Federal has received mixed comments. Federal Reserve banks generally favored the proposal while the American Bankers Association opposed it. Sen. William Proxmire, (D-Wis.) chairman of the Banking Committee, denounced it. "The net effect of the proposal will be to allow Edge corporations to conduct a domestic deposit business across state lines in contravention of the spirit of the McFadden Act branching restrictions."

Sen. Adlai Stevenson (D-I11) praised it and recommended that Edge corporation customers be required to do no more than half of their business internationally. Yesterday, the Fed's board of governors rejected a three-quarters business criterion, based on either purchases or sales of goods and services Chairman G. William Miller stressed the need for a simple eligibility test and suggested the criterion be lowered to two-thirds of a bank's business.

In other action yesterday, the Fed adopted a compromise regulation on disclosure of consumers' liability for unauthorized transfers from electronic fund accounts such as automated teller machines. Until Aug. 1, cardholders will have no liability limits due to loss or theft.

On that date, card issuers may elect whether to inform their customers that their potential liability will increase from $50 to $500 if they fail to report the loss or theft within two lays. However, cardholders could not be held liable if they were not informed.

As of May 1980, notification of liability will be mandatory. The Fed reasoned that some card issuers may find it cheaper to absorb any losses between August and May than to notify all their customers.

Finally, it decided to open negotiations with the Federal Deposit Insurance Corp. for the purpose of supplementing weekly sample reports from member banks with data from 100 mututal savings banks. This proposal is part of a larger effort to collect information from more financial institutions in order to get a more accurate measurement of the money supply.