Iran emerged from years of being considered a pariah state at the weekend after the United States, European Union and United Nations lifted sanctions linked to its nuclear program under an international deal which involved Germany.
Iran was the key to stabilizing the Middle East, referring to conflicts in Syria and Yemen, the minister, Frank-Walter Steinmeier, said.
"We need Iran to calm the conflicts and re-establish stability in this crisis-hit region. And I hope Iran is ready for this," Steinmeier told foreign journalists.
Steinmeier said calming the war in Syria was central to solving Europe's refugee crisis, which has prompted deep divisions within the EU on how to share the burden of accommodating the influx.
Gulf Arab neighbors, including Saudi Arabia, accuse Iran of backing rebels in Yemen and pro-government militias in Syria. A mostly Arab coalition led by Saudi Arabia launched a military offensive against Iran-backed Houthi rebels in Yemen in March.
Tensions rose further this month when Saudi Arabia executed a prominent Shi'ite Muslim cleric, prompting an angry reaction from Shi-ite Iran.
Steinmeier said these tensions would not disappear soon but it was possible to build trust between the two regional rivals.
"Neighborly tensions, like those between Saudi Arabia and Iran, will not turn into friendship overnight," he said.
"In a first step, a lot would be achieved if both sides brought the current situation under control, not let it escalate, and talked to each other," he said.
"I am very confident that this new beginning of German-Iranian relations will be filled with substance," Steinmeier told foreign journalists in Berlin.