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The major futures indexes are indicating a rise of 0.9 percent, or more than 200 Dow points.
U.S. crude was higher by 10 percent, or $2.08 at $22.44 in electronic trading on the New York Mercantile Exchange. It climbed 61 cents on Monday to $20.39.
Brent crude, the standard for international pricing, picked up $2.02 to $29.28 per barrel.
In Asia, Hong Kong's Hang Seng added 1.1 percent.
Markets in Tokyo and Shanghai were closed for a holiday.
In Europe, London's FTSE added 1.2 percent, Germany's DAX rose 1.5 percent and France's CAC jumped 1.5 percent.
This is another busy week for markets, with a slew of corporate earnings reports due, including more than 150 companies in the S&P 500. On Friday, the government will also show how many jobs were lost during April.
|I:DJI||DOW JONES AVERAGES||35061.55||+238.20||+0.68%|
|I:COMP||NASDAQ COMPOSITE INDEX||14836.991139||+152.39||+1.04%|
In Monday's session, the S&P 500 ended 0.4 percent higher after erasing an early loss of 1.2 percent. The Dow Jones Industrial average edged 0.1 percent higher and the Nasdaq composite, which is loaded with technology stocks, rose 1.2 percent.
Microsoft climbed 2.4 percent. Airline stocks sank after famed investor Warren Buffett's Berkshire Hathaway disclosed that it sold all its stakes in American Airlines Group, Delta Air Lines, Southwest Airlines and United Airlines.
American Airlines fell 10.6 percent for the largest loss in the S&P 500. United, Delta and Southwest all lost 7.4 percent or more.
The Associated Press contributed to this article.