The chairman of the Federal Reserve Board said yesterday that economic growth could drop as low as 2.5 percent next year as a result of White House efforts to fight inflation and save the dollar.

The prediction by G. William Miller is the lowest so far from a government official. Miller said the economy would grow between 2.5 and 3 percent.

Many economist do not think a growth rate that low will create enough jobs to keep unemployment from rising. Many also think that if the government tries to keep the economy growing that slowly the nation could slip into a recession.

However, Miller said in an interview, there is no reason to think that slower growth next year will cause the unemployment rate to rise above 6 percent. The unemployment rate has hovered around 6 percent all year and was 5.8 percent in October.

He admitted that the Federal Reserve and the administration are walking a tight line in trying to fight inflation without causing a recession.

Since late April the Federal Reserve has been raising interest rates to cut down on borrowing and reduce the rate of growth of the money supply. Last week, as part of a co-ordinated program to prop up the dollar, the central bank took further steps to raise interest rates sharply and further restrict the availability of bank credit.

Miller hinted yesterday that the administration and the Fed are willing to take further tighteneing steps to combat inflation and the side in the dollar's value, but was not specific.

He said his revised growth estimate - earlier he and most admistration officials had been talking about 3 percent to 3.5 percent next year - is the result of the heavy doses of monetary tightening the Fed has already applied as well as "any other followup that may be necessary."

Miller said he is confident that the economy will not slip into a recession because nearly all indicators show that the economy is still strong and that there are no bottlenecks that could cause sudden retrenchment on the part of businesses or consumers.

He said the economy appeared to grow more briskly in September and October than officials thought it would, even though the Federal Reserve had been raising interest rates steadily. "That makes us think that we are not likely to overshoot," that is, raise interest rates so much that the economic expansion is killed.

He also noted that the impact of higher interest rates on the average consumer has been exaggerated. He said that while consumers are paying higher finance charges for automobile and installment purchases, most of the reason finance charges are higher is that the cost of the products consumers are buying has increased, forcing them to take out bigger loans.