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The drill, which ended on Friday, involved about 31,000 troops, as well as fighter jets, ships and 3,000 vehicles.
Russia has been strengthening its military presence near its borders. In February it held a combat-readiness exercise involving 8,500 troops in a southern region near areas of eastern Ukraine held by pro-Russian rebels.
"What we shouldn't do now is inflame the situation further through sabre-rattling and warmongering," Mr Steinmeier said in an interview to be published in Germany's Bild am Sontag newspaper.
"Whoever believes that a symbolic tank parade on the alliance's eastern border will bring security is mistaken.
"We are well-advised to not create pretexts to renew an old confrontation," he said, adding that it would be "fatal to search only for military solutions and a policy of deterrence".
The exercise in Poland, which takes place every two years, was intended to test Nato's ability to respond to threats, and to allay fears in eastern Europe since Russia's annexation of Crimea.
Nato spokesperson Oana Lungescu said the alliance's actions were "defensive, proportionate, and in line with our international commitments".
She said the alliance had maintained dialogue with Russia through the Nato-Russia Council, although practical co-operation had been suspended, following the annexation of Crimea in 2014.
In an interview with the Bild newspaper on Thursday, Nato Secretary General Jens Stoltenberg said Russia was seeking to create "a zone of influence through military means", with "massive militarisation" at Nato borders.
Russia has repeatedly said that the presence of Nato troops near its borders is a threat to its security.