“I believe deeply that it’s very important to the United States, to the economic health of the United States, that we maintain a strong dollar,” Mr. Geithner said, according to news reports.

Some analysts, however, believe that behind closed doors, policy makers in Washington are happy to see a slow and steady depreciation of the dollar. The weak dollar makes American products cheaper overseas, buoying sales, and makes imports more expensive, encouraging consumers at home to buy American.

On Tuesday night, the president of the Federal Reserve Bank of Dallas, Richard W. Fisher, seemed to hint at that view, saying the drop in the dollar’s value had not been “disorderly” and that rates were likely to remain low for an extended period, Reuters reported.

“Sentiment is still negative, and the comments of the Federal Reserve have only fanned the flames,” said Marc Chandler, the global head of currency strategy at Brown Brothers Harriman.

As the dollar fell, gold reached $1,117.40 an ounce at the stock market’s close on Wednesday, setting another record high as hedge fund managers and wealthy speculators continued to buy the precious metal.

The Dow Jones industrial average ended trading up 44.29 points, or 0.43 percent, at 10,291.26. The broader Standard and Poor’s 500-stock index rose 5.50 points, or 0.5 percent, to 1,098.51, and the Nasdaq composite index jumped 15.82 points, or 0.74 percent, to 2,166.90. Crude oil settled at $79.28 a barrel, up 23 cents, on the New York Mercantile Exchange.

The zeal from strong trading days in Europe and Asia seemed to help perk up Wall Street. The FTSE 100 in Britain closed 0.69 percent higher, the DAX in Germany climbed by 0.98 percent and the CAC 40 in France increased by 0.76 percent. The Hang Seng in Hong Kong rose by 1.61 percent, while the Nikkei in Japan was flat.