The first visit by a German president to Russia since 2010 comes as ties between the two countries remain strained over Russia's annexation of Crimea in 2014 and the subsequent uprising in eastern Ukraine that the West claims is backed by Moscow.
Steinmeier is a former foreign minister who was actively engaged in Germany's efforts to mediate the Ukraine crisis and has long called for engaging Russia.
"We both believe that the current state of affairs cannot satisfy us and should not satisfy us," Steinmeier said following talks with Putin in comments translated into Russian.
Putin for his part said Moscow was ready to develop ties with Germany, adding that German businesses were interested in expanding their footprint in Russia.
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"Despite some certain political difficulties Russian- German ties are not at a standstill," he added.
Earlier today Steinmeier spoke with former Soviet president Mikhail Gorbachev, 86, soliciting his advice on how to improve ties between the two countries.
"I come during times in which German-Russian relations have become difficult," Steinmeier said.
"I see it as my responsibility to contribute to make sure that this doesn't stay this way forever."
Steinmeier also visited Russia's top rights group Memorial and attended a ceremony for the Russian state's return of a cathedral building to the Protestant church.
He praised the handover of the cathedral, which was seized by the Soviets in 1938, and said he hoped that the church would continue to serve as a "place of encounter" between Orthodox and Lutheran Christians as well as Russians and Germans.
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