Federal Reserve Board Chairman Paul A. Volcker triggered a sudden slide in the dollar yesterday after warning there could be "a very sharp decline" in the international value of the dollar because market psychology could "change rapidly."

Volcker, in response to a question from Rep. Connie Mack (R-Fla.), told the House Budget Committee that he sees some merit in trying to devise ways of managing the international monetary system that would achieve greater stability in exchange rate relationships.

When the substance of what he said reached the financial markets, the dollar immediately dropped about 2.5 pfennigs to 3.38 West German marks, and as much as 7 pfennigs in an hour. The close was 3.43 marks. Before Volcker's testimony, the dollar had been strong, touching 3.45 marks -- up from 3.41 on Tuesday. Other currencies reacted in the same way. The French franc closed at 10.46, up from 10.43 Tuesday. In London, the dollar gained slightly against the British pound, with sterling slipping to $1.055 from $1.059 late Tuesday. But sterling rose to $1.069 from $1.056 in the United States.

A Federal Reserve official said that Volcker, who has testified four times in the last two weeks, was not intending to say anything different about dollar prospects than he had said before. But the exchange markets, already somewhat on edge because of the uncertainty over recent intervention by central banks, reacted dramatically.

Volcker was making a point that he and other officials have been stressing: part of the dollar's strength is attributable to a willingness of foreigners to invest in the United States, based on a belief that the U.S. recovery is strong, and that it is a good place to invest.

If that mood changes, and foreigners cut back their investment, Volcker said, the dollar could tumble quickly. And in that case, he added, the United States -- which depends on the foreign funds to help finance the budget deficit -- is not prepared for the consequences.

The Fed chairman didn't forecast such a development, but the fact that he would discuss it at all was bearish news, as far as the markets were concerned. Coupled with a warning that the United States might not be able to sustain its growth rate, and that a sharply lower dollar would add to inflationary risks, it was enough to generate a selling wave.

"One of the things keeping the dollar high is the strength of the GNP," one currency dealer told the Dow Jones news service. He said that a rise in the U.S. inflation rate "would start moving the dollar out." On the question of reforming the international monetary system to achieve more stable exchange rates, Volcker made clear that he was pessimistic on the prospects that the United States and other major nations could agree on setting up a "managed" exchange rate system. "Everybody loves stable exchange rates," the Fed official said, but he wondered who would maintain them.

It was clear, he added, that the burden of maintaining stable exchange rates shouldn't fall on one country alone: "That seems to be the nut of the international monetary problem." Mack's question had been whether Volcker thought it wise to join in or set up something akin to the European Monetary System that regulates allowable fluctuations among European currencies.

Volcker said that there could be useful studies on reaching a "consensus about managing the international monetary system" in a way that would reduce the fluctuations in rates among the European currencies, the dollar and the Japanese yen.

Reagan administration officials make clear that they prefer the present system, which leaves it to supply and demand factors to adjust relative currency values. Treasury officials also appear to have resisted pressures from Volcker, as well as from friendly European governments, for more "forceful" exchange market intervention last week.

The administration has also rejected suggestions, such as one made by former Treasury official C. Fred Bergsten in earlier House Budget Committee testimony this week, to move toward a regime of "target zones" for the dollar, the German mark, and other key currencies. Under "target zones," the major nations would seek to avoid movement of their currencies outside a fairly wide zone of change, say plus or minus 10 percent.