The pan-European STOXX 600 index traded 2.4 percent higher on Tuesday, with the U.K.'s benchmark, internationally focused FTSE 100 up 2.5 percent.
"Markets are bouncing, and can bounce further but the clouds on the horizon are dark, and they're real," Kit Juckes, strategist at Societe Generale, said in a note on Tuesday.
The dollar index, which tracks the greenback against a basket of major currencies, declined dearly on Tuesday, after four days of gains.
U.S. data due on Tuesday include the third estimate for first quarter economic growth, the Case-Shiller Index and consumer confidence. First quarter growth is seen being revised up slightly to 1 percent quarter-on-quarter.
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