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London's benchmark FTSE 100 index won 0.6 percent to 6,071.6 points compared with Monday's close.
In the eurozone, Frankfurt's DAX 30 rallied 1.0 percent to 10,598.1 points and the Paris CAC 40 advanced 0.7 percent to 4,596.6.
Spain's IBEX 35 index jumped 0.9 percent to 9,453.5 points.
The Spanish stock market had slumped by 3.6 percent on Monday following an election that has left the eurozone's fourth-largest economy in political limbo.
Meanwhile other European indices fell into the red in late trading Monday as shares in energy companies tanked on sliding oil prices, analysts said.