BRUSSELS—The European Union’s new foreign-policy chief said the bloc would try to step up cooperation with Russia and Iran over Syria, signaling a shift in Europe’s efforts to end the war there.

The comments by Federica Mogherini, the EU foreign-policy chief, came after European foreign ministers on Monday threw their support behind a United Nations effort to negotiate a military “freeze” in Syria, starting in the besieged city of Aleppo.

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