This was the seventh straight session in which the Dow rose or fell by triple digits, the sign of a highly indecisive market. Analysts said there was no conviction behind the advance; it was just a reaction to the market's recent sharp drop.
Analysts also cautioned that the gain was vulnerable to the next batch of news that says the economy remains fragile.
"It is just a very oversold market in the short term," said Arthur Hogan, chief market analyst at Jefferies & Co.
The Dow had its eighth-biggest one-day point gain ever, rising 346.86, or 4.6 percent, at 7,938.79, according to preliminary calculations. The gain offset much of the Dow's 406-point loss over the previous two sessions. It was also the Dow's biggest one-day point gain since July 29, when it rose 447.49.
The broader market also soared. The Nasdaq composite index rose 41.70, or 3.6 percent, to 1,213.76. The Standard & Poor's 500 index advanced 32.64, or 4 percent, to 847.92.
"When we post a rally like this, no one wants to get in the way, because we have been selling stocks for three years. After one of these selloffs, everyone hopes and prays it is the bottom. So that is why we get these exaggerated moves," Hogan said. "But the fundamental macroecnomic problems are still going to be there when we wake up."
Depressed prices after Wall Street's latest drop drew buyers even as the market digested a report by the Institute of Supply Management that manufacturing activity contracted in September after seven straight months of growth.
The decline in the group's index of business activity to a reading of 49.5 is significant because any figure below 50 shows contraction.
Stocks were rising before the report's release and while they faltered somewhat afterward, analysts said rumors about the index had circulated before trading began and therefore it was not viewed as negatively as might be expected.
Also Tuesday, the Commerce Department reported that construction spending dropped 0.4 percent in August. The dropoff, chiefly because of cutbacks in private builders' projects including offices, industrial complexes and hotels, met analysts' expectations and followed a 0.1 percent decrease in July.
Analysts said the fact that stocks were able to advance after the release of the reports shows that investors were assessing them without alarm, interpreting them to mean the economy is at least not weakening.
The reports "are not bad. They're just saying we're treading water, and I don't think that surprised anybody," said Alfred E. Goldman, chief market strategist at A.G. Edwards & Sons Inc. in St. Louis.
Some of Tuesday's buying could also be attributed to a practice called short covering in which investors who sold shares figuring the market was going to keep dropping are forced to buy stock to cover their positions when the market advances.
Gainers included Sun Microsystems, up 17 cents at $2.76. The comp,0125
any disclosed late Monday that its earnings for the year would be higher than expected due to adjustments in its accounting.
Pepsi Bottling Group also rose, up $1.60 to $25, after it reported early Tuesday that its net income grew 19 percent in the third quarter.
Shares of Vivendi Universal and News Corp. advanced after a deal was announced for Vivendi to sell its Italian pay-TV business, Telepiu, to News Corp. Vivendi rose 86 cents to $12.25. News Corp. gained 88 cents to $20.13.
But Ford Motor slipped 10 cents to $9.90 after a pair of analysts cut their price targets on the automaker because of concerns about its pension liabilities and operational difficulties.
Advancing issues outnumbered decliners by 9 to 5 on the New York Stock Exchange, where volume was heavy.
The Russell 2000 index, the barometer of smaller company stocks, rose 5.80, or 1.6 percent, to 368.07.
Overseas, markets were mixed with Japan's Nikkei stock average closing down 2.4 percent. In Europe, Germany's DAX index gained 3.5 percent, France's CAC-40 climbed 1.8 percent, and Britain's FTSE 100 rose 2 percent.