The Supreme Court has been asked to step into a major controversy among federally regulated financial institutions over the use of new technologies by millions of depositors, savers and credit-union members to transfer or withdraw funds estimated to total $10.5 billion.

The case involves pre-arranged automatic fund transfers from savings to demand accounts to cover checks or maintain specified balances in checking accounts; remote service units, used by savings and loan associations to render off-the-premises services, including withdrawals, and sharedrafts, the credit-union version of checks.

The heart of the issue is whether existing federal laws permitted various agencies to adopt regulations approving each of the devices or whether new legislation is needed.

The agencies are the Federal Reserve System and the Federal Deposit Insurance Corp., which approved rules for fund transfers in May 1978; the Federal Home Loan Bank Board, which adopted its rules in the same month, and the National Credit Union Administration, which acted in December 1977.

The actions variously pleased and displeased interests with stakes in the same turf, resulting in three separate suits filed in the U.S. District Court here.

In one suit, the American Bankers Association challenged the NCUA; in a second suit, the American Bankers Association's benefactors, the Fed and the FDIC, were challenged by the United States League of Savings Associations; in a third, the league's supporter, the FHLBB, was challenged by the Independent Bankers Association of America.

Each case ended in victory for the government, with Judge Aubrey E. Robinson Jr. ruling for the NCUA and FHLBB, and judge Oliver Gasch ruling for the Fed and the FDIC.

Last April, however, both judges were reversed by the U.S. Court of Appeals here. In an unsigned opinion, the court said that fund-transfer technology has outpaced existing laws, leaving it "no option but to set aside the regulations" despite "enormous investments" by financial institutions in, and wide public reliance on, the technology.

But the court stayed its ruling until Jan. 1, 1980, in order to enable Congress to pass new legislation if it cares to.

In a petition to the Supreme Court, Solicitor General Wade H. McCree Jr. said the ruling, if not reversed by the justices or undone by legislation, will "put an end to services that have proved to be efficient for financial institutions and beneficial to large numbers of the general public."

As of last July, he said, depositors held more than $7.1 billion in fund transfer programs. More than $2.6 billion was in savings accounts, accessible through remote units, and in excess of $783 million was in share draft accounts.

The appeals court "provided no analaysis to show that the administrative agencies had erred in concluding that existing legislation provides a sufficient basis for these services or that the District Court had misconstrued the separate statutory provisions," McCree said.

In opposing review, the ABA protested the unfair competition that sharedraft accounts provide to commercial checking accounts, because the former earn interest while the latter are barred by law from doing so.