After rallying more than 100 points early on, the Dow Jones Industrial Average extended its gains in the wake of U.S. economic data that showed the Institute for Supply Management's index inching up to 48.6% in March from 48.3% in February.
The reading topped the forecasts of analysts polled by MarketWatch, who expected the index to slip to 47.0%.
Separately, the Commerce Department reported U.S. construction spending fell 0.3% in February, less than the 1% drop predicted by economists.
The Dow industrials were recently up 220.73 points at 12,483.62, with all but one of its 30 components posting gains, led by Citigroup Inc., up 7.3%.
The S&P 500 added 21.88 points to 1,344.58, while the Nasdaq Composite advanced 42.12 points to 2,321.22.
On the New York Mercantile Exchange, crude-oil futures fell $1.64 to $99.94 a barrel, while gold futures dropped $35.20 to $881.00 an ounce.
An added positive is the favorable reception to Lehman's offering. "It's three times oversubscribed; people are interested in investing in Lehman," said Art Hogan, chief market strategist at Jefferies & Co., of the New York-based brokerage.
Lehman saw its shares add 9.6% after it announced plans to offer $4 billion in convertible preferred shares.
Also higher, UBS gained 11.2% in early action after its disclosed $19 billion write-down, and that it would need to issue another $15 billion in shares and that its chairman was exiting.
Deutsche Bank reported a $3.9 billion write-off, mostly on leveraged loans, commercial real estate and Alt-A exposure.
"It's not just a U.S. problem, it's the European banks' turn to say, 'Yeah, we had a little exposure there too,' " said Hogan, who also pointed to an index showing confidence among Japanese manufacturers at a four-year low as putting U.S. economic woes in perspective.
Later Tuesday, U.S. automakers are due to report their monthly sales figures, with Edmunds.com seeing a 13% drop in March sales. Chrysler, held by Cerberus Capital Management and Daimler, is expected to post the worst figures of the Big Three.
International stock markets were mixed. Chinese stocks suffered, with the Shanghai Composite losing 4.1%. But buoyed by the UBS news, the Swiss SMI rose 2%.
U.S. stocks on Monday finished the worst quarter in nearly five years with a solid advance.
By Kate Gibson