Chan warned against judging the quarter based on the small number of companies that have reported at this early stage.
The Nasdaq composite index soared 54.42 points, or 1.8 percent, to 3,042.82. Apple, the most valuable company by market value, rose 5.1 percent after five straight days of losses that wiped out about $60 billion in market value.
There was mixed earnings news after the closing bell. IBM, the most expensive stock in the Dow, fell in after-hours electronic trading after the technology company reported revenue that fell short of analysts' forecasts. The shares were down $4.75 to $202.70. If the stock opens down that much on Wednesday that alone will pull the Dow down 36 points. Yahoo and CSX both rose after reporting earnings, but neither is in the Dow. Intel, which is, fell 80 cents to $27.67.
In Spain early Tuesday, the government sold more than €3.2 billion ($4.2 billion) in short-term debt, more than had been expected. The yield on Spain's 10-year government bond fell to 5.88 percent from 6.10 percent early Monday, a sign of improving confidence in the country's finances.
The cost of insuring Spanish debt against default fell back from a record high, another sign that the auction reassured bond investors. The cost of insuring €10 million in Spanish debt for five years had soared to €522,000 per year on Monday. After Tuesday's auction, it fell to €489,000.
Italy's benchmark stock index rose 3.7 percent. France's and Germany's gained 2.7 percent. The broad STOXX 50 index of European shares rose 2 percent, the most since November.
In the United States, the rally followed a batch of mixed economic news. The number of permits requested by homebuilders for future projects reached a 3½-year high, an indication that the housing market might stop weighing down the economy. But builders broke ground on homes at a slower pace in March.
Factory output fell after four strong months of gains.
Among the other companies that reported earnings:
— Forest Laboratories Inc. rose 4 percent after it weathered competition from generic drug makers better than analysts had expected.
— Regional bank Comerica Inc. gained 3.5 percent after improving credit conditions limited its loan losses and allowed it to increase lending.
AP Business Writer Matthew Craft in New York contributed to this report.
Daniel Wagner can be reached at www.twitter.com/wagnerreports.
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