NATO "has intensified operative and combat training activities, including nuclear weapons use procedures," Russian Defense Minister Sergey Shoigu said.
The war games include an "offensive portion... that looks to me like a rehearsal of an attack," General Curtis Scaparrotti said.
Moscow has confirmed close-up footage of a helicopter misfiring into onlookers is genuine but has denied the timing.
The Baltic NATO ally summoned Russia's envoy to demand an explanation, but Moscow claims the incursion was an emergency call which is being "politicized."
After turning down the invite and sending Russia's foreign minister instead, the Kremlin unveiled Putin's alternative plans.
The Zapad drill on Europe's borders could include almost 10 times the permitted number of troops, provoking fears among NATO members.
Russia has said its new military drill is not aimed at any particular state, but the planned map shows the hypothetical enemy is in Poland, Latvia and Lithuania.