"We took note of this with a great deal of attention. We will now see with our Russian partners which concrete steps will follow from this proposal," foreign ministry spokesman Martin Jaeger said.
"I am very confident that our Russian partners will give concrete content to what was proposed in a general way yesterday and from there a further dialogue in this regard will then conceivably be possible."
Medvedev made the proposal on Thursday during a visit to Germany in his first major foreign policy speech since succeeding Vladimir Putin last month.
"In the current conditions, with no-one wanting war in Europe and with all of us having the experience of the 20th century, such an accord would have all the chances of success," he said in Berlin.
In a hard-hitting speech, the Russian president also warned that attempts to expand NATO eastwards towards Russia's borders would "spoil" relations between Moscow and the West "in a radical way" for years to come.
Jaeger said this should not be read as a sign that Russia is calling for an end to the military alliance that was originally formed during the Cold War as a counterweight to the Soviet Union.
"What we did not read into the speech yesterday, although many commentators
interpreted it in this way, is that Russia is rejecting NATO or is calling for the dissolution of NATO.
"That is too simple an interpretation," Jaeger said.
Moscow has been angered in recent years by the prospect of NATO moving into a region it regards as its traditional sphere of influence and notably opposes extending membership to Ukraine as a threat to Russian security.
Jaeger described Medvedev's visit to Germany and talks with German Chancellor Angela Merkel as a useful indicator of the future foreign policy of Putin's successor.
"We could learn a lot, and also with regard to the future, about Germany and Europe's relationship with Russia," he said.