Oil rose towards $50 a barrel on Wednesday for the first time in seven months on expectations of shrinking supply due to well fires in Canada and other disruptions.
Comments from policymakers in recent days have raised expectations of a rate hike in June, much sooner than previously thought.
"We've had some good economic data and investors are coming around to the fact that higher rates in a small measured dose isn't the end of the world, but is a measure of confidence in the economy," said Andre Bakhos, managing director at Janlyn Capital LLC in Bernardsville, New Jersey.
Traders are now pricing in a 37.5% chance for a June rate hike, up from just 4% last week, according to CME Group's FedWatch tool.
At 9:36 a.m. ET (1336 GMT) the Dow Jones industrial average was up 93.58 points, or 0.53%, at 17,799.63, the S&P 500 was up 10.14 points, or 0.49%, at 2,086.2 and the Nasdaq Composite was up 17.40 points, or 0.36%, at 4,878.46.
Nine of the 10 major S&P sectors were higher, with the energy index's 0.76% rise leading the gainers.
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Oil majors Exxon and Chevron were up about 0.7%.
So far in 2016, the S&P 500 is up about 2%, while the Nasdaq is down 3%.
Wall Street surged more than 1% on Tuesday and the Nasdaq had its strongest day in three months.
Fed speakers scheduled to speak later on Wednesday include Federal Reserve Bank of Philadelphia President Patrick Harker, Minneapolis Fed Chief Neel Kashkari and Dallas Fed Chief Robert Kaplan.
Easing concerns over several major global risks helped stock markets worldwide rise robustly for a second day.
Traders say several polls show Britain will vote strongly to stay in the European Union, while Euro zone finance ministers agreed with Greece and the International Monetary Fund on a deal that will address Athens' requests for debt relief.
Shares of Computer Sciences soared 31.9% to $47.10 after Hewlett Packard Enterprise said it would spin off and merge its struggling IT services business with the company. Hewlett Packard Enterprise was up 12.6% at $18.24.
Alibaba Group was down 2.6% at $78.89 after the company said it was being investigated by the U.S. SEC over whether its accounting practices violated any federal laws. Yahoo, in which Alibaba own a stake, was down 2.2% at $36.68.
Sarepta Therapeutics jumped 24% to $22.87 after the FDA delayed its decision on the company's muscle-wasting drug.
Apparel retailer Express slumped 15.2% to $13.59 after its results missed expectations.
Advancing issues outnumbered decliners on the NYSE by 1,884 to 735. On the Nasdaq, 1,437 issues rose and 717 fell.
The S&P 500 index showed 24 new 52-week highs and no new lows, while the Nasdaq recorded 44 new highs and five new lows.