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London's benchmark FTSE 100 index dropped 0.40 percent to open at 6,593.78 points compared with Monday's close.
Frankfurt's DAX 30 lost 0.23 percent to 11,058.04 points and in Paris the CAC 40 shed 0.42 percent to 4,849.39.
Losses were far less acute than on Monday, when the Frankfurt and Paris indices both closed down more than 3.5 percent over fears that Greece may be heading for a eurozone exit.
Greece on Tuesday looked set to miss an IMF payment and default, with a defiant Athens urging Greeks to reject creditors' demands for tough reforms in a weekend referendum, despite warnings that this would lead to a chaotic Greek exit from the eurozone.