A critical dike broke along the Elbe River in Germany on Monday, and several more threatened to break, flooding a number of villages, triggering thousands of evacuations and blocking major train arteries between Berlin and much of the rest of Germany.

This comes as expectations that more than a week of flooding in Central Europe would start to ease were dashed after fresh rainfall swelled rivers in the Czech Republic again. Forecasters were expecting more thunderstorms in parts of southern Germany on Monday, just as recovery...