BERLIN—German Chancellor Angela Merkel's government is quietly pursuing a more conciliatory course with Russia, a shift that reflects a strategy to protect national business interests and assuage a public increasingly wary of antagonizing Moscow.

While continuing to warn Russian President Vladimir Putin against threatening Ukraine, Ms. Merkel—who earlier said Russia could face massive political and economic damage for its annexation of Crimea—is now emphasizing the need for more dialogue with the Kremlin.

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