BERLIN—The British government should be given time to weigh the consequences of an exit from the European Union, a close aide to German Chancellor Angela Merkel has said in the first sign that Berlin didn’t see Britons’ vote to leave the bloc as irrevocable.

“Politicians in London should have the possibility to think again about the fallout from an exit,” Peter Altmaier, the chancellor’s chief of staff, told a consortium of German regional newspapers in an interview to be published Monday.

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