The Cooperative Longbow/Cooperative Lancer 2009 command-and-staff exercise runs from May 6 to June 1.
Moscow has said the event has increased international tensions in the wake of last year's armed conflict between Russia and Georgia over South Ossetia.
"I think they will add nothing to the bank of pan-European security but will on the contrary increase tensions," RIA Novosti reported Medvedev as saying about the NATO exercises.
More than 1,300 troops from 19 NATO member or ally states were originally scheduled to participate, but Kazakhstan, Latvia, Estonia, Moldova, Serbia and Armenia withdrew, the Russian news service reported.
For its part, NATO has said the exercise had been planned before the confrontation between Russia and Georgia and was not aimed at provoking Russia.
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