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Near 9:38 a.m. ET, the Dow was up 236 points, the S&P 500 was up 25 points, and the Nasdaq was up 64 points.
Stocks closed lower on Wednesday.
Yesterday's three-hour-long outage at the New York Stock Exchange was likely triggered by a software upgrade, according to Bloomberg, citing two people familiar with the situation.
The halt was the biggest disruption to the US stock market since the Nasdaq blacked out in 2013.
Chinese stocks rebounded sharply, and the Shanghai Composite had its biggest one-day rise since 2009.
In economic data, initial jobless claims rose more than expected (297,000 versus 275,000 estimated,) and economists say it's a seasonal anomaly.
"In one line: Seasonal chaos begins; expect more volatility for the next couple of weeks," wrote Pantheon Macroeconomics' Ian Shepherdson in a note to clients.
Barclays noted: "Between the holiday week and the seasonal retooling shutdowns at auto factories that are typical this time of year, we are inclined to look through the volatility in this morning's report."
Crude oil prices rallied more than 3% following the selloff earlier this week that took West Texas Intermediate crude futures to a three-month low. WTI climbed to as high as $53.53 on Thursday morning.
In earnings, PepsiCo reported second-quarter profits that topped estimates, helped by growth in its beverages business. The company posted adjusted earnings per share of $1.33 (versus $1.24 estimated, according to Bloomberg) on sales of $15.92 billion (versus $15.8 billion.)
In company news, Procter & Gamble is merging 43 of its brands with Coty for $12.5 billion. The company accepted an offer for brands in its cosmetics and fragrances business, which include CoverGirl makeup and Gucci fragrances.
Coty shares tanked more than 9% in early trading, while Procter & Gamble rallied by about 1%.
Goldman is recommending selling Shake Shack shares. Analysts cut their outlook on the stock in a note on Thursday, saying that it's too expensive, and the IPO lockup expiration is coming July 29.