The Federal Reserve Board, in an attempt to improve short-term control of the money supply, yesterday decided to eliminate most of the two-week lag between the time a financial institution receives a deposit and the time it must place a portion of it with the Fed as a reserve.

Some Reagan administration officials, including Treasury Secretary Donald T. Regan, have been pressing the Fed to shift from the present lagged reserve accounting approach to so-called contemporaneous reserve accounting. The officials and most monetarist economists maintain the switch will greatly improve the Fed's ability to hit its money supply targets on a month-to-month or quarter-to-quarter basis.

Secretary Regan, who called yesterday's action "welcome news," has blamed the Fed's inability to control money growth month-by-month for causing the current severe recession.

However, none of the five Fed governors who voted for the change "in principle," including Chairman Paul A. Volcker, claimed it would provide more than a small marginal improvement in money control. Two governors, Lyle E. Gramley and Nancy H. Teeters, opposed the change on the grounds it would increase the volatility of interest rates and would cost financial institutions many millions of dollars to implement.

The purpose of the change is to make financial markets respond more quickly to Fed efforts to bring money growth back on track if it starts increasing either too rapidly or too slowly.

Even most monetarist economists agree, however, that deviations in money growth lasting only a few months do not affect economic activity unless the Fed fails to get money growth back on track within a reasonable time.

The board acted over the nearly unanimous opposition of about 160 depository institutions that commented on a staff proposal to make the change. The banks and thrift institutions argued the costs they would incur to collect necessary information about deposits more quickly would not be worth it in terms of better control of money.

"The Federal Reserve Board's decision will produce only marginal improvement in monetary control at best and will certainly lead to serious cost increases for banks and other reporting entities of all sizes," the American Bankers Association said in a statement after the Board's decision.

As with most aspects of monetary policy implementation, the nature and timing of reserve requirements is a highly technical matter. A financial institution that accepts deposits, say, in a checking account, must set aside a portion of them in the form of a non-interest bearing deposit at a Federal Reserve bank. Institutions with more than $26 million in such checking, or transactions accounts must deposit 12 percent of them with the Fed.

At present, the institutions keep track of their deposits for each seven-day period ending on Wednesday. They then are not required to set aside the reserves associated with those deposits until a comparable seven-day period two weeks later.

The proposal adopted yesterday would lengthen from one week to two weeks the period in which deposits are counted. Each deposit period would end on Monday, and there would be only a two-day lag, until Wednesday, before the associated reserve accounting period ended. Thus, most of the 14 days over which deposits and required reserves are averaged would overlap.

Eliminating the lag, at least in theory, will encourage the banking system to respond more quickly to the week-to-week actions by the Fed through which it seeks to regulate growth of the money supply by adding and subtracting reserves from the system. The Fed can reduce the availability of reserves by selling government securities to bond dealers who pay by drawing down their deposits at banks and such action usually causes key short-term interest rates to rise. The rise in rates discourages borrowers and a drop in the growth of loans slows the creation of money through the banking system.

The staff suggested not changing to contemporaneous reserve accounting until May of next year, but Chairman Volcker, who said he "reluctantly" supported the majority favoring the change, was bothered by the long delay. The Board will meet again to work out final details.