The Federal Reserve Board apparently alarmed by the further slide of the dollar, acted on its own to stem the continuing decline yesterday by raising interest rates in the United States.

The move, decided by the board in a relatively close 4-to-3 vote, came with only token advance consultations with the Carter administration, some of whose top policy-makers were surprised by the Fed action.

White House officials expressed mixed reactions to the new move. Although the administration wants to deal with the dollar slide, it also fears that higher interest rates could choke off the domestic recovery.

The Fed's action was regarded as extraordinary. The central bank has raised interest rates for international reasons only four times in the past 15 years - all in response to major balance of payments crises.

What the board did yesterday was to increase its discount rate - the interest it charges on loans to member banks - to 6 1/2 per cent, up from the 6 per cent level that has prevailed since last October.

The rationale behind the move is to make the United States a more attractive market for investment in comparison to Europe and Japan - thus attracting more investment from abroad and stemming the flow of American investment elsewhere.

Officials hope that if the investment situation is turned around, it will improve the nation's balance of payments position somewhat and result in an increase in the value of the dollar in the foreign exchange markets.

The problem is the shift also will tend to raise interest rates for domestic borrowers and add to U.S. inflation. Carter administration officials have cautioned that if interest rates rise too sharply, the recovery could be hurt.

The action marked the third major step in three weeks that the United States has taken to stem the decline in the dollar. President Carter issued a statement of concern about the currency situation last month. And only last Wednesday, the United States announced it was ready to begin intervening in the markets to prop up the dollar.

Yesterday, before the later-evening announcement of the Fed's action, the dollar slid further on the major foreign exchange markets, although at a more modest pace than in previous days. On Wednesday, the dollar had declined 2 full percentage points in a single day.

In a statement announcing its action, the board described the currency market turmoil in unusually strong language, saying the recent disorder in the markets "constitutes a threat to orderly expansion of the domestic and international economy."

At the same time, the board expressed "hope that the need for the increase will prove temporary." The governors added that "the condition of the [U.S.] domestic economy is sound, and that credit supplies to sustain economic expansion will remain ample."

It was not fully clear how well the Fed coordinated its action with the administration. W. Michael Blumenthal, the Secretary of the Treasury, issued a statement later saying he was "consulted" about the decision and that "we understand the rationale for the move." However, other top officials were taken by surprise.

The decision to raise the discount rate was backed by the present Fed chairman, Arthur F. Burns, and three other governors - Henry C. Wallich, the board's top international expert; Stephen S. Gardner and Philip E. Coldwell.

Two members opposed the move - J. Charles Partee and David M. Lilly. Lilly's term on the board expires Jan. 31. A seventh member, Philip C. Jackson Jr., was not present at the meeting.

International authorities said after the announcement that raising the discount rate is a "standard step for a central bank to take when its currency is declining. The action was regarded as partly symbolic, but analysis stressed that the United States "needed to demonstrate a tough stance" to reverse the dollar's slide.

There was no immediate indication how soon the board would move to lower the discount rate again. Outside analysts suggested the Fed governors may want to wait until they are sure the alarm over the dollar overseas has subsided.

The Fed has not used the discount rate to help prop up the dollar since 1968, when the gold markets were hit by a rash of speculation. Before that, it employed the measure only during 1963, 1964 and 1967. The last date marked the early British devaluation of the pound. The discount rate has remained at 6 per cent since last Oct. 26, when it was raised from a 5 3/4 per cent level imposed in August. The last time the rate was 6 1/2 per cent or higher was in February and March of 1975, when it reached 6 3/4 per cent.