New York Federal Reserve Bank President Anthony Solomon yesterday delivered a careful warning -- obviously on behalf of the entire Federal Reserve system -- that a purely monetarist approach to the problem of inflation is doomed to failure.

In a speech to the Financial Analysts Federation, Solomon -- whose New York bank presidency ranks him on the Federal Open Market Committee second only to Fed Chairman Paul A Volcker -- said "it would be a mistake to assume that slowing monetary growth by itself offers a simple or painless, purely 'technical,' solution to our inflation problem."

Solomon's speech also amounted to a clear restatement of the Federal Reserve's concern that tax cuts will precede budget cuts, boosting the federal deficit and shaking financial market's confidence in the future.

Noting that long-term interest rates had not come down much since the beginning of the year, he said "we cannot expect to avoid unpleasant interest-rate pressures within a context of constrained money growth unless these markets become convinced that the deficit is, in fact, coming under control."

Solomon made it plain that the Fed endorsed the overall goals of President Reagan's four-point economic recovery program, the last component of which calls for slowing the rate of growth of the money supply. "We all now recognize that the time has come to seize the day, to take concerted action needed to change the course of events," Solomon said.

But Solomon's detailed speech clearly indicates that the Fed is worried that a few influential officials in the Reagan administration may be overemphasizing the anti-inflationary role that monetary policy can play, thus de-emphasizing other needed elements of a balanced program.

In addition to monetary restraint, Solomon stressed the need for a " responsible and disciplined fiscal policy" that would avoid excessive deficits. This would require tailoring tax cuts to actual spending reductions. Volcker repeatedly has stressed that he would prefer that Congress cut the budget first and then proceed to tax cuts.

Solomon said that financial markets are waiting to see firm evidence that Congress actually will cut government spending "in amounts sufficient to moderate government credit demands in the face of prospective tax cuts, and they also await evidence that inflation will cool. These markets live on anticipations of the future."

The New York Federal Reserve Bank president told the analysts that despite theories espoused by monetarists, "Our secular inflation of the last 15 years is the result of complex economic and social forces . . . The task of curing inflation will thus involve more than purely technical adjustments in the monetary policy field."

He observed that experience of industrial economies abroad similar to our own "confirms the suspicion that slowing monetary growth by itself may not be enought to control price inflation within acceptable periods of time and without unacceptable side effects."

If the circumstances are unfavorable -- such as excessive demand in the private sector, or cost pressures originating from the government sector -- "the effort to cool inflation through monetary policies alone may ultimately fail because the side effects will not prove to be acceptable," Solomon said. "Fundamentally, this is why it is no easy matter to eliminate inflation simply through the in-itself-not-technically-difficult process of slowing monetary growth."