They are being conducted on military ranges in Belarus, western Russia, the Russian exclave of Kaliningrad, and in the Baltic Sea.
In Minsk, Col Vladimir Makarov, a Belarusan military spokesman, said that all 3,000 Russian military personnel in the country would leave when the war games conclude on Wednesday.
"It is a normal practice for any country to hold such exercises".
While the Baltic nations fear the Zapad maneuvers may lead to a surprise Russian attack, the exercises have also been criticized by Belarusian opposition leaders.
"We are not threatening anyone", Oleg Voinov, an adviser to the Belarusian Defense Minister, told journalists Thursday.
The military exercise is called Zapad 2017, which means "west" in Russian, and it has been used earlier for military drills conducted by the eastern giant in 1981 and 1999.
"The degree of mobilization is really impressive", Mr. Soloch said on private Radio Zet.
Earlier this week Jens Stoltenberg, NATO general secretary, said Russian Federation has every right to hold drills, but accused it of using "loopholes" to avoid scrutiny.
Russia's Defense Ministry said Thursday that elite parachute units in several Russian cities had been placed on alert to be deployed during the exercises. "The main goals are to improve interoperability among the military staff, harmonize troops management systems and provide commanders of various levels of importance with an opportunity to train their skills in planning military events and managing troops based on the experience received during modern armed conflicts", said the Russian defence ministry.
There is also unease in Kyiv, and Ukraine is now conducting its own military exercises, called "Unflinching Tenacity", scheduled to end Friday.
The defense Ministry of Belarus refutes claims that the exercises "West-2017" involved 100 thousand military.
Russian President Vladimir Putin is going to attend the joint Russia-Belarus "Zapad" 2017 military drills which have recently started, the Kremlin has confirmed.
Others think fears of Russian aggression are out of proportion to the potential threat posed by the war games. "Russians will not seek confrontation, because they know that North Atlantic Treaty Organisation will be watching this event closely and is certainly ready to react", said Kestutis Girnius, a Vilnius University political analyst.
Information for this article was contributed by David Filipov, Ishaan Tharoor and Michael Birnbaum of The Washington Post; and by Yuras Karmanau of The Associated Press.