Russia says it is watching with great concern after the US put 8,500 troops on alert to be ready to deploy to Europe in case of an escalation in the Ukraine crisis.
Russia has started making combat readiness inspections in its southern military district, which borders Ukraine.
RIA news agency cited Russia's military as saying on Tuesday that inspections has involved more than 6,000 troops.
The Kremlin earlier said it was watching with great concern after the United States put 8,500 troops on alert to be ready to deploy to Europe in case of an escalation in the Ukraine crisis.
Kremlin spokesman Dmitry Peskov accused Washington of fuelling tensions over Ukraine - repeating Moscow's line that the crisis is being driven by US and NATO actions rather than by its own build-up of tens of thousands of troops near the Ukrainian border.
Western states accuse Russia of planning a new attack on Ukraine, which it invaded in 2014.
Moscow denies any such plan but says it could take unspecified military action unless demands are met, including a NATO promise never to admit Kiev.
NATO said on Monday it was putting forces on standby and reinforcing eastern Europe with more ships and fighter jets. Russia denounced the moves as Western "hysteria".
Peskov said President Vladimir Putin would talk this week to his French counterpart Emmanuel Macron, who is also planning to speak with Ukrainian President Volodymyr Zelenskiy.
Russia is awaiting a written US response this week to its list of security demands it has presented, some of which Washington has dismissed as non-starters.
Peskov said the US troop alert did not affect negotiations because the current phase of talks had been completed.