"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 Art Hogan, chief market strategist at Jefferies & Co..
He also pointed to an index showing confidence among manufacturers at a four-year low as putting U.S. economic woes in perspective.
The Dow Jones Industrial Average climbed 168.62 points to 12,431.51 in the opening moments.
The S&P 500 added 18.53 points to 1,341.23, while the Nasdaq Composite advanced 36.80 points to 2,315.90.
Commodities prices came under pressure as the dollar showed strength against major currencies.
On the New York Mercantile Exchange, crude-oil futures fell $1.80 to $99.70 a barrel, while gold futures dropped $30.90 to $885.30 an ounce.
"There's obviously a global impact to this credit problem, making the dollar show surprising strength and causing a sell-off in gold," Hogan said.
An added positive is the favorable reception to Lehman's offering. "It's three times oversubscribed; people are interested in investing in Lehman," said Hogan of the New York-based brokerage.
Lehman saw its shares add 7.7% after it announced plans to offer $4 billion in convertible preferred shares.
Also higher, UBS gained 9.8% 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.
"Despite these massive losses, hopes abound that further write-downs may be limited, allowing financial conditions to improve," said Benjamin Reitzes, economist at BMO Capital Markets.
Amid all the news in the financial sector, the dollar rose, notably against the euro.
There's data to come from the Institute of Supply Management, which may report that manufacturing sentiment dropped further below the 50% level indicating economic expansion. Also out is data on construction spending for February.
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