President Reagan blamed the Federal Reserve. Fed officials blamed the administration. And meanwhile, interest rates climbed still higher, with major banks pushing their key prime lending rate to 17 percent last Wednesday.

The president changed tactics on Thursday and embraced the Fed's monetary policy at a televised press conference. But words alone are unlikely to bring interest rates down.

Few analysts are willing to bet on what will. The cost of money is now extraordinarily high both in relation to inflation and to the state of the business cycle. This year's combination of rising interest rates, exploding money growth and deepening recession has baffled economists and policy makers.

Interest rates generally fall during recession as private credit demands fall off. The drop in inflation over the past year also should have pushed nominal interest rates down by cutting that portion of interest rates that merely compensates lenders for rising prices. Instead, rates are rising, and no one is quite sure why.

For a while last fall, all the economic indicators moved in step and signaled recession. Unemployment rose, production fell and interest rates began to come down, while the money supply stayed flat. But in November, money growth accelerated sharply, and in early December interest rates stopped falling and began to climb.

Such unexpected strength in the financial indicators could have been an early signal that the economy was recovering. In 1980, a rise in the money supply was the first indication that the short, sharp recession of the second quarter was over.

But just as the banks moved the prime up again last week, the Federal Reserve published statistics showing that the current recession worsened at the turn of the year. Industrial output dropped by 3 percent in January, and capacity utilization fell to its lowest level for seven years. Bad weather contributed to the January slump, but it did not account for it all.

While there may be confusion about just why interest rates are rising in midst of recession, there is little doubt among economists that if the rise is not halted, this year's promised economic recovery will not materialize.

Interest rates on short-term Treasury debt are already back up close to their prerecession peaks. Long-term bond rates and mortgage interest rates fell only slightly from their 1981 highs and are fast approaching them again. It was these high rates that precipitated the recession.

Some economists have already revised their economic forecasts downward to show a decline in gross national product in the current quarter that matches the 5 percent annual-rate fall at the end of last year. In his news conference, the president backed off from earlier administration predictions that the economy would pick up briskly this spring.

He commented that "high interest rates present the greatest single threat today to healthy, lasting recovery," and held out hope of more cooperation between the administration's fiscal policy and the Fed's tight money policy. "The administration and the Federal Reserve can help bring inflation and interest rates down faster by working together than by working at cross-purposes. . . . I am sensitive to the need for a responsible fiscal policy to complete a firm, anti-inflationary monetary policy."

Explanations for the upset in financial markets--and therefore recommendations about how to correct it--have centered around the conflict between the administration's growth-oriented fiscal policy and the Fed's tight monetary targets. Some analysts, and Fed Chairman Paul Volcker, stress the role of the large projected budget deficits. These raise long-term interest rates, they argue, by adding to financial market fears of future inflation, and so adding to the "inflation premium" included in the long rates. A huge and growing federal presence in financial markets also contributes directly to raising interest rates by increasing the demand for credit, they argue.

Others put more emphasis on the Fed's tight monetary policy. The present targets for money growth simply do not leave enough room for the economy to grow satisfactorily, economists James Tobin and Lawrence Klein told a congressional committee recently. When recovery starts it will run into this "monetary lid," interest rates will climb automatically as credit demands rise, and the economy will stall, they and others say.

Those who attribute more weight to monetary policy believe that the economy will grow only sluggishly with present Fed policies, almost irrespective of what happens to fiscal policy and the budget deficit. The present run-up in interest rates--even before the economy has begun to recover--illustrates just how effectively present money policies work to hold down the economy and squeeze out inflation, according to one top Wall Street economist.

Tight money will work to hold down growth by keeping interest rates relatively high, he says, and can override the attempts of Congress and the administration to boost the economy through fiscal policy.

If the administration and Congress try to raise growth through running a big deficit, interest rates will rise all the more and offset the additional demand from the deficit. It may be possible to bring interest rates down through reducing the deficit substantially and easing credit market pressures. But the tax increases or spending cuts that reduce the deficit will themselves dampen the economy, the same analyst argues, by reducing the spending power of taxpayers in the one case or beneficiaries of government programs in the other.

In this view, the Fed is the real culprit for high interest rates and the economy's poor growth performance, as well as the hero of the anti-inflation battle. If more growth rather than less inflation is the objective, then the Fed should raise its money targets, accept somewhat more inflation than otherwise, and give the economy room to recover.

But, Volcker argues, financial market concerns about inflation are now so great that it is no longer possible to bring down interest rates and stimulate recovery by increasing the money supply. When money growth accelerates, interest rates rise because of market fears of future inflation, rather than falling in response to easier credit. In recent weeks rising money supply has indeed coincided with higher interest rates.

Conversely, the drop in money announced on Friday could lead to a decline in rates.

However, this does not suggest that all the Fed needs to do to bring down interest rates is tighten the monetary screws. An alternative explanation for the market's apparent perversity is that financiers view an unexpected rise in the money supply as a signal for the Fed to tighten up. Market participants expect the central bank to move swiftly to choke off any sudden increase in the money supply--by rationing credit and raising rates--so they push rates up themselves as soon as the increased money numbers are announced.

While an announced drop in the money supply could work in the opposite direction, the underlying tension between a constricted money supply and an economy that is trying to grow will put a limit on how far rates can drop, the Wall Street economist said.

A longer, deeper recession will bring rates down. But higher money targets could also do the trick, and without the cost in terms of lost output and employment. Such a policy would risk more inflation, however, and the Fed is unlikely to embark on such a path, especially while the administration's fiscal policy is also going for more growth rather than less inflation.