In the United States, an indicator of consumer purchasing from the Department of Commerce showed that overall retail sales in May declined by 0.2 percent, a smaller decline than the 0.5 percent fall that had been forecast by analysts surveyed by Bloomberg. The figure was a reversal of the 0.3 percent rise in April, and it was the first monthly decline after 10 consecutive increases.

When gasoline sales are excluded, retail sales fell by 0.3 percent, according to the government figures, also the first time this year that figure turned negative.

“The recent trajectory of consumer spending excluding the gasoline category is cause for concern,” said Joshua Shapiro, the chief United States economist for MFR Inc. “With higher gas prices eating into the income available for discretionary spending, the consumer faces stiff headwinds. This underscores how absolutely key it is that the labor market continue to improve.”

Analysts suggested that the markets on Tuesday were propelled partly on economic data from China that pointed to an increase in industrial output and a rise in consumer prices that was in line with forecasts.

Keith B. Hembre, the chief economist and chief investment strategist at First American Funds, said the data from China was “not a big downside surprise” and led to stronger market sentiment in Asia and Europe that was passed on to the United States.

“It is a pretty powerful relief rally,” he said.

The Dow Jones industrial average closed up 123.14 points, or 1.03 percent, to 12,076.11. The Standard Poor’s 500-stock index rose 16.04 points, or 1.26 percent, to 1,287.87. The Nasdaq composite index average climbed 39.03 points, or 1.48 percent, to 2,678.72.

The stock market in the United States had risen slightly on Monday after six weeks of losses partly fueled by concerns over the pace of the global and domestic economic recovery, and concerns over euro zone sovereign debt challenges.

Another issue that has been lingering in the markets has been the protracted political wrangling over the national debt ceiling in the United States. Moody’s Investors Service said earlier this month that it might downgrade the United States credit rating if lawmakers did not raise the ceiling “in coming weeks.”

On Tuesday, the chairman of the Federal Reserve, Ben S. Bernanke, warned about the consequences of a continued delay, saying even a short suspension of payments on principal or interest on the Treasury’s debt obligations could cause severe disruptions in financial markets.

“In debating critical fiscal issues, we should avoid unnecessary actions or threats that risk shaking the confidence of investors in the ability and willingness of the U.S. government to pay its bills,” Mr. Bernanke said in a speech in Washington.

He also said that interest rates soar as investors lose confidence, as seen in a number of countries recently.

“Although historical experience and economic theory do not show the exact threshold at which the perceived risks associated with the U.S. public debt would increase markedly, we can be sure that, without corrective action, our fiscal trajectory is moving us ever closer to that point,” he said.

Still, the stock market had little discernible reaction to the remarks and surged throughout the day.

Among the leading shares was the Best Buy Company, which rose more than 4 percent after reporting net earnings of $136 million, or $0.35 a diluted share, for its fiscal first quarter ended May 28. That compared with $155 million, or $0.36 a diluted share, for the same period in 2010.

On the Dow, Caterpillar was up 2.79 percent, Home Depot rose more than 4 percent and Intel rose more than 2 percent. “The markets have been in a corrective stage, and I think we have reached levels now that perhaps we can see some renewed interest in terms of valuations,” said Peter Cardillo, the chief market economist for Avalon Partners.

Mr. Cardillo said the United States data was “not that bad,” reflecting the impact on consumer prices from higher gasoline prices and the situation in Japan.

“None of them suggest that we are headed for a double-dip recession,” Mr. Cardillo added.

Another economist noted that the retail sales data and other reports Tuesday painted a “disappointing picture” of the domestic economy.

Steven Ricchiuto, the chief economist for Mizuho Securities USA, cited a National Federation of Independent Business consumer confidence index and a government report that said wholesale prices rose in May.

“Small business optimism continues to remain in recession territory with no sign of firming, while consumers continue to consolidate spending even after energy prices have eased,” he said in a research note

The Producer Price Index, which reflects commodity prices for manufacturers, rose 0.2 percent in May, according to seasonally adjusted figures provided by the Bureau of Labor Statistics. The increase was slightly higher than the 0.1 percent rise forecast by analysts, and it came in below the 0.8 percent rise in April.

The May increase in the finished goods index was attributed mostly to prices for finished energy goods, which rose 1.5 percent, the eighth consecutive monthly advance. The food component of the index declined 1.4 percent.

The core index for finished goods, which excludes the volatile energy and food components, also rose 0.2 percent, in line with forecasts and slightly less than 0.3 percent rise in April, the government figures showed. It was the sixth consecutive rise in the core producer prices index.

Gasoline prices moved up 2.7 percent in May, the statistics showed.

When calculated on a year-over-year basis, the total finished goods index was 7.3 percent higher in May.

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