The pan-European STOXX 600 index was down 0.1% by 0714 GMT, with shares in Frankfurt falling 0.2% and Paris dipping 0.1%.
UK and US markets are closed for a holiday, keeping trading activity muted across the board.
The STOXX 600 was on course to record a 2.6% rise in May as economies gradually reopened after lockdowns, while governments and central banks reiterated support to help the recovery.
Deutsche Bank slipped 1.7% after a report said the U.S. Federal Reserve told the German lender it was failing to address persistent shortcomings in its anti-money-laundering controls. (Reporting by Sruthi Shankar in Bengaluru; Editing by Sriraj Kalluvila)