The Russell 2000, which contains many energy and biotech names, closed mildly lower to hold within 20 percent of its 52-week high. In intraday trade, the small-cap index briefly fell more than 20 percent from its 52-week intraday high, in bear market territory.
The Dow Jones industrial average and Nasdaq composite remained more than 10 percent below their 52-week intraday highs, in correction territory. The S&P 500 held within 10 percent of its 52-week high.
"I still think ultimately you need to be a seller on the rallies," said John Caruso, senior market strategist at RJO Futures. He cited "uncertainties around the world" and expectations of a "weak corporate earnings cycle."
Alcoa was scheduled to report earnings after the bell, ahead of major financial firms' results due later in the week.
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The Dow transports closed down half a percent, well off session lows.
"Overall, given the fact that oil is at (multi-year) lows, our markets have held up fairly well," said Randy Frederick, managing director of trading and derivatives at Charles Schwab.
Declines in commodities pressured European stocks to turn lower and remain more than 15 percent below their 52-week intraday highs, in correction territory. The German DAX held more than 20 percent below its 52-week high, in bear market territory.
Helping stocks stabilize overnight was news the People's Bank of China raised the midpoint fix for the yuan against the U.S. dollar to 6.5626. Weakness in the yuan and concerns about further devaluation weighed heavily on global equities last week.
"The communication of the Chinese peg is probably as (important) piece of data that we get. We've had two upticks in the peg even though it didn't help Chinese (stocks)," said Art Hogan, chief market strategist at Wunderlich Securities.
The Shanghai composite lost more than 5 percent Monday, while the Hang Seng closed more than 2.5 percent lower.
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U.S. stocks closed sharply lower Friday, ending the first trading week of the year with losses of nearly 6 percent or more, their worst week since 2011. The Dow and S&P 500 had their worst start to a year in history.
"I think in the near-term it was overdone. It's not going to be a one-way trade. The conditions that undermined equity prices last week haven't gone away," said Mark Luschini, chief investment strategist at Janney Montgomery Scott.
Treasury yields held steady, with the 2-year yield near 0.94 percent and the 10-year yield around 2.17 percent.
The U.S. dollar held about 0.3 percent higher against major world currencies, with the euro below $1.09 and the yen at 117.75 yen against the greenback.
In economic news, Atlanta Fed President Dennis Lockhart said in a Reuters report there may not be enough fresh data on inflation to support another U.S. interest rate hike by March, but the economy should grow enough to support more hikes over the rest of the year.
He also said that a slowdown in China and plunging oil prices are now the main risks for what is an otherwise promising outlook for the U.S. economy.