European stocks closed fractionally higher Tuesday, rebounding at the last minute after being pressured most of the session by the energy sector after Iran poured cold water on hopes for an output cap at a meeting of major oil producers this week.

U.S. stocks swung higher Wednesday after OPEC took an important step toward a cap on crude-oil output. The Organization of the Petroleum Exporting Countries reached an "understanding" to limit crude production and is considering cutting production to between 32.5 million to 33 million barrels a day, The Wall Street Journal reported.

The overnight rally in oil prices amid reports that oil producers finally agreed to cut production levels sent Asia markets higher on Thursday. In Japan, the Nikkei 225 rallied 1.55 percent, while the Topix index was up 1.08 percent. Across the Korean Strait, the Kospi advanced 0.82 percent. Hong Kong's Hang Seng index was up 0.38 percent. Mainland Chinese markets were also higher, with the Shanghai composite up 0.22 percent and the Shenzhen composite adding 0.15 percent.