"It's all about earnings today," said Peter Cardillo, chief market economist at Avalon Partners.
"However, some of the early strength may fade, as some of the geopolitical problems heat up again, with the dollar resuming its slide and oil prices picking back up," Cardillo said.
The Dow Jones Industrial Average climbed 54.7 points, or 0.4%, to 13,621.7, with 26 of its 30 components in positive territory, led by American Express Co. , up 1.9% after the credit-card and travel-services company tallied an 11% rise in profits for the third quarter.
The S&P 500 rose 6.28 points, 0.4%, to 1,512.61, while the Nasdaq Composite advanced 20.93 points, or nearly 0.8%, to 2,774.86.
Volume on the New York Stock Exchange topped 316 million, and advancing stocks outran declining issues 2 to 1. On the technology-laden Nasdaq, more than 663 million shares exchanged hands, and advancing stocks beat declining stocks more than 3 to 1.
"Favorable earnings results from Apple, DuPont and AmEx overnight still managed to overshadow fresh concerns about credit related write-offs in the financial sector," said analysts at Action Economics.
"Media reports overnight focused on Merrill Lynch's third-quarter earnings announcement (scheduled for Wednesday), mulling more write-offs related to credit issues," said the Action Economics analysts.
Stock of the New York brokerage was off 1.8%.
Ahead of the opening bell, blue-chip DuPont , the nation's second-largest chemical maker, said its earnings rose 8.5% in the third quarter, bolstered by international and agriculture growth.
Shares Apple rose about 7% after the consumer-electronics company reported a 67% increase in earnings in the fourth quarter on solid iPod and iPhone sales. .
Other companies reporting earnings include AT&T Inc. , which matched expectations. .
Shares of conglomerate 3M Co. led the few Dow decliners, its stock falling 0.9%.
Oil giant BP Plc reported a 29% drop in third-quarter profit, but still beat forecasts, after a widely leaked internal company memo warned of "dreadful" results.
On the New York Mercantile Exchange, crude-oil futures for December delivery fell 60 cents to $85.42. .
Elsewhere on the NYME, gold futures fell 60 cents to $759.40. .
The dollar was mixed, slipping against the euro but gaining on the yen, with the dollar index, which measures the U.S. unit against a basket of major currencies, was down about 0.6% at 77.600, compared with 77.955 late Monday. .
Overseas, European shares advanced as a recovery in industrial and mining shares helped restore confidence after the previous day's sharp sell-off.
On Monday, Wall Street bounced back, with technology shares leading the way, with the Dow adding 44 points, the Nasdaq gaining 28 points and the S&P rising 5 points.
By Kate Gibson