"(The markets) were way oversold," said Louis Giglio, a senior portfolio manager at American Express Financial. "I think some people might have woken up today and thought 'Hey, there might be some good deals out there.'"
The Nasdaq rose 254.37, or 8 percent, to close at 3,459.48; the largest percentage increase and second-highest point gain in its history. The Standard & Poor's 500 index gained 44.43, or 3 percent, to 1,422.45.
Two stocks rose for every one that fell on the Nasdaq Stock Market, as 39 stocks set new highs and 194 stocks that touched new lows.
The Dow Jones industrial average rose 227.89 to 10,527.13, led by Intel and Hewlett-Packard.
Some strategists remained cautious, saying they wanted to see more positive days before deciding the markets have successfully weathered the volatility.
"We may be entering a more constructive period for stocks prices, but I wouldn't be surprised to see more down days," said Phil Dow, a market strategist at Dain Rauscher Wessels.
Byron Wien, chief U.S. strategist at Morgan Stanley, said the price rebounds were strong, but investors need to see "more convincing volume" before concluding that the downturn may be over.
"People have in their heads that the Fed will tighten one more time (in June) and then stop because the economy is slowing, but I don't trust it," he said.
The Nasdaq and Dow posted light trading volumes, indicating that large institutional investors may prefer to wait until the volatility subsides before diving into the trading fray.
Dain Rauscher Wessels' Dow said that the rough times are not over. "I still think the market will confound people looking for relief in the short term," he said, adding that he believes, along with other market watchers, that the Federal Reserve meeting June 28 will reveal all.
At the end of regular trading, Intel closed up $8.19 at $125.75. The chipmaker has slashed list prices for its desktop and mobile processors, although many of the discounted chips remain in short supply.
Microsoft inched up $1.94 to $63.38.
The CNET tech index gained 176.22, or 7 percent, to 2,628.53. Winner trounced losers, with 97 of the 99 stocks in the index rising, one falling and one remaining unchanged.
All 18 sectors tracked by the index rose. Semiconductor equipment companies posted the sharpest gains, climbing 12 percent. Computer distributors were the smallest gainers, climbing 2 percent.
Among members of the CNET tech index, Ciena and Vitesse Semiconductor posted strong gains.
Ciena rose $21.81, or 22 percent, to $121.50, and Vitesse gained $8.94, or 20 percent, to $53.50. Siebel Systems rose $19.63, or 19 percent, to $125, while Inktomi gained $16.31, or 16 percent, to $118.
The Philadelphia semiconductor index gained 100.64, or 11 percent, to 1,010.30, led by chipmaker Teradyne, which rose $11.81 to $84.56.
In other market related news, a newspaper reported that NTT DoCoMo, Japan's largest mobile phone company, is in talks to buy as much as 20 percent of U.S.-based VoiceStream Wireless for about $4.68 billion. Shares of VoiceStream rose $19.50, or 19 percent, to $119.88.
Handspring, the handheld computer start-up launched by the founders of the PalmPilot, said today it has lowered the price range for its initial public offering to between $17 and $19 from between $19 and $22. Shares of rival Palm rose $2.63 to $24.