Some of the things "bothering markets yesterday were China and collapsing commodity prices and both of those have given us some relief and when I look at China I don't look at the Shanghai market. I look at the Hong Kong market," James Meyer, chief investment officer at Tower Bridge Advisors, said of the morning rally.
The Hang Seng closed up 0.72 percent, while the Nikkei plunged 4 percent and the Shanghai Composite extended recent losses to fall below the psychologically key 3,000 mark, down 7.6 percent. However, European stocks surged, with the DAX up nearly 5 percent.
Crude oil futures settled up $1.07, or 2.80 percent, at $39.31 a barrel. Brent traded more than 1 percent higher to above $43 a barrel.
For the rally to be real "we have to end strong and follow-through tomorrow," Meyer said.
Read More A Dow Theory 'sell' sign has the market nervous
In early trade Tuesday, Dow futures spiked above 600 points, implying an open of more than 450 points.
U.S. stock index futures extended gains after the Chinese central bank announced plans early in the morning ET to cut its one year lending rate to 4.6 percent, which the People's Bank of China said was provide long-term liquidity and help support the economy.
Read MoreMore selling ahead but bull market 'not dead yet'
"I'm looking for every reason to be a buyer," said Nick Raich, CEO of The Earnings Scout, who remains bearish on equities. "We're not upgrading our view at this point until we see topline growth... until then it's going to be hard to sustain a rally."
For Tuesday's open, the New York Stock Exchange invoked Rule 48 for the second day in a row, Dow Jones reported.
The exchange used the rule before Monday's open after futures for several major averages hit limit down.
Before this week, Rule 48 was most recently invoked in January 2015. In all, Rule 48 has been invoked 67 times since it was approved in 2007, according to an NYSE spokeswoman. The goal of the rule is to ease market volatility.
Read MoreWhat is Rule 48?
Stocks plummeted on Monday, with the S&P 500 joining the other major averages in correction territory. Nine of the 10 sectors are in correction territory, with consumer staples less than 1 percent away.
The Dow had its biggest intraday swing ever, falling as much as 1,089 points in the open on Monday. U.S. stocks closed more than 3.5 percent lower, off session lows in high volume trade as fears of slowing growth in China pressured global markets.
Cumulative trade volume was 13.94 billion shares as of 4:00 p.m. ET, the highest volume day since Aug. 10, 2011. Composite trade volume on the New York Stock Exchange was 6.57 billion shares, the heaviest since Oct. 27, 2011.
High-frequency trading accounted for 49 percent of Monday's total trade volume of 14.2 billion shares, according to TABB Group. Average daily trade volume month-to-date is 7.5 billion shares, with high-frequency trading accounting for 49 percent. During the peak levels of high-frequency trading in 2009, about 61 percent of 9.8 billion of average daily shares traded were executed by high-frequency traders.
Trade volume was tepid throughout most of Tuesday's session before accelerating into the close for a cumulative 10.3 billion shares as the major averages sold off.
Housing data out Tuesday missed expectations slightly but continued to indicate strength in the market. New home sales figures for July came in at an annual rate at 507,000. The Case-Shiller home price indices for June showing home prices rose less than expected.
In other economic news, the Conference Board's consumer confidence indicator for August rose to 101.5, beating expectations.
"So far it doesn't appear that we've had any disease from the foreign markets (in the economy)," Luschini said.
The U.S. dollar traded about 1 percent higher against major world currencies, with the euro lower near $1.15 and the yen trimming losses against the greenback near 118 yen.
Treasury yields jumped from lows touched Monday, with the 10-year Treasury yield at 2.09 percent, off highs of near 2.14 percent, and the 2-year note yield at 0.60 percent after trading near 0.64 percent.
The Treasury Department auctioned $26 billion of two-year notes at a high yield of 0.663 percent, lower than the previous July auction. Demand was below average and the lowest since October.