Despite its earlier statement that a tough anti-inflation program and an emergy bill would take the pressure off interest rates, the Carter administration is relying more heavily than ever on monetary policy to combat the twin problems of inflation and a declining dollar.

Tuesday night, in a move carefully coordinated with the White House, the monetary policy-making Federal Open Market Committee voted quitely in Washington to direct its New York trading desk to further raise short-term interest rates, Federal Reserve sources said.

President Carter announced yesterday a series of steps to bolster the U.S. dollar, many of which also portemd higher interest rates for the U.S. economy.

Although the decline in the dollar is due to many factors - including a substantial U.S. trade deficit - the primary cause is higher inflation in the United States than in most of the major industrial countries.

So far, despite concerted attempts by the Federal Reserve, the nation's central bank, to fight inflation and restrain the growth of the money supply, prices and the money supply (checking accounts plus currency in circulation) keep rising apace.

In late April, the central bank's key interest rate, the so-called federal funds rate, was 6.75 percent. Yesterday, market analysis said, it appeared the Fed was trying to keep that interest rate - the one banks charge each other for overnight loans of excess reserves - at 9.5 percent.

While the central bank has boosted interest rates sharply during the past six months, the money supply has continued to grow and business and consumer demand for loans has remained high.

In September, for example, the money sipply grew at an annual rate of 141 percent. The Fed is trying to keep money growing at a rate between 4 and 6.5 percent.

Economists agree that the growth of the money supply is an important determinant of both inflation and economic growth, although they disagree on just how important money growth is.

Clearly the Carter administration, shocked by the sharp decline of the dollar last week as well as the collapse of stock prices in the wake of the announcement of its much-touted anti-inflation program, decided it had to take together steps to reduce money growth and, in turn, inflation.

Federal Reserve Board chairman G. William Miller said in a telephone interview, that by boosting the discount rate (the interest the Fed charges member banks for a loan) from 8.5 percent to 9.5 percent: the Fed is demonstrating "its determination to continue to pursue to the degree needed" its efforts "to tamp down the growth of inflationary forces."

He said the coordinated efforts between the independent Fed and the administration show a "government united" with a "full arsenal of weapons" to fight inflation, including a hold-down on federal spending and the voluntary anti-inflation program as well as a "monetary policy that has been moving in the right direction for some time."

He said the markets yesterday appeared to concur with his judgement. The dollar rallied, stock prices rose by a record amount, and the bond market boomed.

Short-term interest rates were higher yesterday than 30-year rates, an indiction that those who invest their money for a long time "have a changing long-term view of inflation prospects," Miller said.

With short-term interest rates rising to nearrecord highs, however, and a Fed action to clamp-down on the amount of money banks have to lend (by raising socalled reserve requirements on large certificates of deposit the Fed could pull up to $3 billion of lendable funds out of the banking system the nation could soon be walking on the precipice of the recession.

The high rates could choke off the economic expansion.

But Miller said the actions impose "no danger of recession" and by showing further determination to fight inflation "improve the prospects for avoiding a recession."