After two huge sell-offs in a row, U.S. stocks were all over the map on Tuesday. Investors blamed the wild moves on a combination of interest-rate fears, computer-driven trading and the obscure volatility funds that use leverage.

The Dow Jones industrial average opened with a big whoosh lower, then rallied all the way back. The Dow closed 567.02 points higher at 24,912.77 and rose as much as 600.48 points. At its session low it was down by 567.01 points. It traded in a range of 1,167.49 points. DowDuPont was the best performer on the Dow, rising nearly 6 percent.

The ended 1.7 percent higher at 2,695.14 with tech as the best-performing sector. The Nasdaq composite gained 2.1 percent to close at 7,115.88.

"I thought we were going to see the bottom within five minutes of when we opened. I think that's basically what we're seeing," said Ed Keon, portfolio manager at QMA, the quantitative and dynamic asset allocation business of PGIM. "At these levels, stocks represent pretty good value and we're adding to equity exposure." Keon said it's too early to call a bottom but he expects that the worse is over.

European markets also fell. The German Dax dropped 2.3 percent, while the French CAC 40 fell 2.4 percent. In Asia, the Japanese Nikkei 225 plunged 4.7 percent, while the Shanghai composite pulled back 3.4 percent.

On Monday, the Dow dropped 1,175.21 points, having briefly declined more than 1,500 points during the session. Other major indexes closed sharply lower. The sell-off kicked into action on Friday, after the latest nonfarm payrolls report saw interest rates in the U.S. jump.

"We think this is an interruption [of the bull market] rather than the start of a bear market," said Craig Callahan, founder of ICON Advisers. "We didn't see any of the typical conditions you get for a top."

This pullback came after a rip-roaring start to the year for stocks. The Dow and S&P 500 notched all-time highs as well as sharp gains for January.

"Widespread and excessive optimism left stocks vulnerable to increased volatility as bond yields have moved off their lows," said Bruce Bittles, chief investment strategist at Baird. "While there is some early evidence that selling pressures are becoming exhausted, and stocks could soon see relief, the broad market is seeing meaningful deterioration."

While there was no particular piece of news that pushed major U.S. indexes deep into the red on Monday, the recent moves in the bond market have added volatility and concern to the market.

The benchmark 10-year yield traded around 2.75 percent on Tuesday; it began the year trading near 2.4 percent.

The Cboe Volatility index — widely considered the best fear gauge on Wall Street — broke above 50 in early trading Tuesday before sliding down to 29.69. It closed at 37.32 on Monday.

"When you have volatility measures as low as they have been, ... that lack of volatility can turn into a risk," said Lance Humphrey, portfolio manager at USAA. "What we saw wasn't that surprising."

The surge in volatility also triggered massive selling in other volatility instruments.

The VelocityShares Daily Inverse VIX Short-Term exchange-traded note (XIV), which allows traders to bet against the VIX, lost nearly all of its value on Tuesday. Credit Suisse, which sponsors the ETN, said it will end trading on the XIV on Feb. 20.

—CNBC's Patti Domm contributed to this report