Sentiment was boosted Monday by two surveys that showed China's manufacturing sector improved last month after prolonged weakness.
The HSBC purchasing managers' index rose to 50.1 points in August, a level that indicates expansion as output and new orders edged up slightly and order backlogs rose at the fastest pace in two years. The official China Federation of Logistics and Purchasing PMI rose to 51.0 from July's 50.3, which was the highest level and biggest increase this year.
Both indexes use a 100-point scale on which numbers below 50 indicate a contraction.
Traders will be waiting for Wall Street to reopen later Tuesday after a three-day Labor Day weekend as well as the latest data from the Institute for Supply Management on U.S. manufacturing for August.
On Monday, Britain's FTSE 100 gained 1.5 percent to close at 6,506.19, thanks to cellphone company Vodafone, which said it was with in talks with Verizon to sell its U.S. mobile business. Confirmation of the $130 billion deal came after trading in London had finished for the day, but Vodafone's shares closed up 3.4 percent on expectations of the purchase.
Germany's DAX index ended the day up 1.7 percent to 8,243.87 while France's CAC-40 jumped 1.8 percent to 4,006.01. Italian and Spanish stocks were also up after surveys showed manufacturing activity rose in the two countries, which are in recession and have been focal points of Europe's debt crisis.
Benchmark crude for October delivery was down $1.01 to $106.64 a barrel in electronic trading on the New York Mercantile Exchange as fears of military strikes on Syria continued to fade. The contract fell $1.15 to close at $107.65 on Friday.
In currencies, the euro rose slightly to $1.3189 from $1.3187 late Monday. The dollar fell to 99.31 yen from 99.56 yen.
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