Russia was behind the murder last month of a former Chechen rebel in Germany, U.S. officials said on Tuesday, rekindling concerns that Moscow is ramping up an assassination campaign against the country’s perceived enemies abroad.

The victim, a 40-year-old Georgian who once commanded forces against Russia during a Chechen uprising, was gunned down in a Berlin park on Aug. 23 on his way to a local mosque. Minutes later, German police arrested a Russian man attempting to leave the scene on an electric scooter after he discarded...