BERLIN—A rebound in Covid-19 cases in Berlin and elsewhere in Europe is fueling concerns among public-health authorities about a second wave of infections following the lifting of lockdowns across the continent.

In Berlin, daily new coronavirus cases shot back up to levels last seen in April after weeks of steady fall. The Berlin state government on Tuesday said it would start imposing fines for violations of a mask-wearing requirement that has been in place for weeks but not enforced.

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