"With the entry into office of President Obama, there is a genuine chance for new cooperation between the United States, the European Union and Russia," Steinmeier said.
"The ghost of the Cold war has been banished... So I would like to say that the extended hand of the US president should be boldly accepted," he said.
US President Barack Obama is due in Moscow early next month for talks with his Russian counterpart Dmitry Medvedev on a successor to a key, Cold War-era disarmament pact, the Strategic Arms Reduction Treaty (START), set to expire in December.
Steinmeier, the Social Democratic candidate for chancellor in September elections, spoke in Moscow ahead of meetings with Medvedev and Prime Minister Vladimir Putin.
"Indecisiveness or bargaining for tactical advantages can again close the window of opportunity," Steinmeier said. "Therefore, I am calling on our partners here in Moscow and all those to whom international security is important: Let's, together, use this unique, historic chance."
The Russian president's proposals for a new global security architecture would be on the agenda at a summit of foreign ministers of the Organisation for Security and Cooperation in Europe (OSCE) in Greece later this month.
Medvedev's proposals for security reform have so far been met with a lukewarm response from the European Union as have Russia's calls for new rules to regulate international energy relations.
But Steinmeier, who is known for favoring strong bilateral ties with Moscow, also hailed as "constructive" Medvedev's calls for a reform of the rules in the energy sector.