HSBC shares were in focus, falling around 3 percent, despite the bank reporting a better-than-expected rise in pre-tax profit for the first quarter of the year, to $7.06 billion.
Meanwhile, German stocks finished around 2.4 percent lower, dragged down by airline Lufthansa, which closed around 2.2 percent down after a reporting first quarter loss that was narrower than expected, but warning that further action was needed to lower costs.
The French CAC also tumbled, to close around 2.1 percent lower.
In Switzerland, UBS shares surged as much as 6 percent on Tuesday after the banking group reported profit for the first quarter that was nearly double that posted in the same period last year.
U.S. stocks traded lower on Tuesday as investors eyed higher bond yields and domestic data for April that could shed light on the timing of an interest rate hike.
Greece in focus
Greek stocks closed 4 percent lower amid conflicting reports on the progress of its loans-for-reform negotiations with its international bailout supervisors.
The Financial Times newspaper reported that the International Monetary Fund (IMF) had said that Greece needed further debt relief, which was denied by German Finance Minister Wolfgang Schaeuble.
Greece itself muddied the water by stating that its bailout negotiations were being delayed by disagreements between the IMF and the European Union.
Spanish jobless falls
On the data front, Spanish unemployment for April fell by 2.7 percent, compared to the previous month.
French budget data on Tuesday morning also showed that the country's deficit had narrowed at the end of March, compared to the year before.
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