The United States and other industrial nations sold more than $10 billion over a six-week period in a successful and coordinated effort to bring down the value of the dollar, the Federal Reserve Bank of New York reported yesterday.

The dollar sales followed the Sept. 22 decision by the so-called Group of Five countries -- the United States, Japan, Britain, France and West Germany -- that other currencies should appreciate in value.

The intervention has continued through November and beyond, but data for this latest period will not be published for another three months. But New York Fed Executive Vice President Sam Y. Cross, who prepared the report on Treasury and Federal Reserve foreign exchange operations for the three months beginning Aug. 1, said in a telephone interview that the dollar has declined 13 percent against the deutsche mark and 16 percent against the yen from Sept. 22 through yesterday.

Since the dollar hit its peaks late in February, the total decline through yesterday has been 27 percent against the mark and 23 percent against the yen. If the pattern continues, these declines in the dollar exchange rate are expected -- with some time lag -- to begin to narrow the American trade deficit.

The Group of Five meeting in September at the Plaza Hotel in New York was initiated by Treasury Secretary James A. Baker III, who concluded with the other nations that the dollar had risen too far and was out of line with underlying economic conditions.

An overvalued dollar, officials agreed, was contributing to the huge U.S. global trade deficit. The American willingness to intervene in foreign exchange markets in a substantial way -- a complete reversal of Reagan administration policy that earlier had endorsed and defended a strong dollar -- was enthusiastically welcomed by the other nations.

The operative language of a communique issued by the G-5 said that "in view of the present and prospective change in fundamentals [in economic conditions], some further orderly appreciation of the main non-dollar currencies against the dollar is desirable."

Cross' report showed that intervention by the United States in the three-month period from August through October was $3.2 billion, all of it coming after Sept. 22. In addition, the other four countries of the G-5 sold about $5 billion. And the central banks of the other western industrial nations sold more than $2 billion.

Even with the heavy selling, the Cross report showed, there continued to be heavy upward pressure on the dollar, as market forces tested to see how persistent the central banks would be in their coordinated selling efforts. It was not until late October, according to the Fed's narrative, when Japan pushed interest rates higher, that "the dollar began to decline particularly sharply against the yen."

Despite denials by officials here, in Japan, and in Europe that there was a coordinated policy to reduce all interest rate differentials compared with the dollar, "the idea persisted, and the dollar declined across the board to close near its lowest levels of the three-month period under review."

According to Cross' report, the G-5 decision had an immediate "announcement" effect on the dollar, even before actual intervention began. The agreement was taken not only as a reversal of the old Reagan position on intervention, but "was interpreted as eliminating the likelihood that the Federal Reserve would tighten reserve conditions in response to rapid U.S. monetary growth."

In the first two weeks following Sept. 22, the United States sold a total of $199 million against German marks and $262 million against the yen, "operating repeatedly and visibly at times when the dollar showed a tendency to rise from the lower levels it had reached."

But by mid-October, the dollar was staging a comeback, in part based on perceptions at that time that U.S. economic activity was picking up. In the third and fourth week following Sept. 22, the United States accelerated its intervention, selling $1.55 billion against the German mark and $618 million against the yen.

In the fifth and sixth weeks, with "a fading of optimism" about the U.S. economic outlook, the pressure on the dollar against European currencies diminished, which allowed U.S. authorities to concentrate on the yen. In that period, sales were only $87 million against the mark and $483 million against the yen.