The 32-member Democratic majority on the House Banking Committee yesterday warned the Federal Reserve against paying interest on member bank deposits without specific authorization from Congress.

Yesterday's late afternoon action by committee Democrats is the latest development in an escalating battle between the central bank and the banking committees over who has the power to direct the spending of the $7 billion in interest the Fed earns each year on its portfolio of government securities.

The Fed is concerned about the large number of banks who are leaving the Fed system - in part because they cannot earn any interest on the dollars they must keep on deposit with the central bank. Most state regulatory agencies allow banks they control to keep their reserves in interest-bearing government securities.

Senate Banking Committee chairman William Proxmire (D-Wis.) and House Banking Committee chairman Henry Reuss (D-Wis.) have told Federal Reserve chairman G. William Miller by letter that only Congress can mandate spending of the $7 billion in interest the Fed earns.

After paying its expenses, the Fed returns to the Treasury the balance of the interest it earns on its securities holdings. Last year it returned nearly $6 billion to the Treasury.

Miller wrote back to Proxmire and Reuss that he thought the question was a legal one and that the Fed is convinced that it already has the authority to pay interest to member banks. But, he said, if both committees disagreed with the Fed's position, it would be "unlikely" that the Fed would go ahead and pay member banks on its own.

Proxmire and Reuss are both sympathetic to the need to keep banks from leaving the Fed system and have promised to hold speedy hearings on a bill to permit the Fed to do so.

But, they argued in their letter to Miller earlier this month, that if the Fed were allowed to spend its money as it desires, congressional control over spending would be eroded and the Fed would become, in effect, a $7 billion spending agency.

Ranking minority member J. William Stanton (R-Ohio) is known to be in sympathy with Reuss's position and has already introduced a bill that would give the Fed authority to pay member banks interest and charge them for services that the Fed now provides free.