Steinmeier elected German president
The Kremlin said in a statement that Russian President Vladimir Putin had congratulated Steinmeier in a telegram and invited him to visit Moscow.
Steinmeier last year drew criticism when he said NATO's decision to stage military manoeuvres in eastern Europe amounted to "sabre-rattling". His Social Democrats prefer a softer stance towards Russia than Merkel's conservatives.
Russia wants the European Union to lift sanctions imposed over its annexation of Crimea and backing of separatist rebels in eastern Ukraine.
The German constitution mandates that a special assembly is convened to elect presidents. It includes 630 lawmakers in the Bundestag lower house and an equal number of representatives from the federal states.
Current President Joachim Gauck steps down on March 18.
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