The war games, dubbed Rapid Trident, kicked off at 9:00 am local time on Monday at the International Peacekeeping and Security Center (IPSC) in Yavoriv in western Ukraine, Ukraine’s Defense Ministry said.
At least 2,000 troops from more than 14 NATO member states and their partners in Eastern Europe attend the exercises, according to the ministry.
The maneuvers will involve military equipment, including armored vehicles, military helicopters and aircraft.
The first part of the annual military exercise will come to an end on July 8.
Conducted annually, Rapid Trident this year involves Ukraine, the United States, Belgium, Bulgaria, Canada, Georgia, The United Kingdom, Moldova, Lithuania, Norway, Poland, Romania, Sweden and Turkey.
Earlier this month, NATO held another 10-day military drill, involving some 31,000 troops from Poland, the US, and 17 other nations in Poland.
Russia, wary of the increased presence of NATO troops close to its borders, threatened to take unspecified measures to respond to the increased activities by the Western military bloc.
NATO has stepped up its military buildup near Russia’s borders since it suspended all ties with Moscow in April 2014 after Crimea re-integrated into the Russian Federation following a referendum.
Ukraine's eastern provinces of Donetsk and Lugansk have witnessed deadly clashes between pro-Moscow forces and the Ukrainian army since Kiev launched military operations in April 2014 to crush pro-Moscow protests there.
The United States and its European allies accuse Moscow of destabilizing Ukraine. Moscow rejects having a hand in the crisis and blames the West for the bloodshed that has so far claimed the lives of more than 9,200 people and left over 21,000 others injured.
A US army commander warned earlier this week that NATO was unable to resist against Russian power in the Baltics.
The commander of US ground forces in Europe, General Ben Hodges, said that Russian forces could capture Estonia, Latvia, and Lithuania "quicker than we could get there to defend them."
On Saturday, a former Russian commander, Admiral Vladimir Komoyedov, said Russia is capable of responding to the increasing NATO military presence by deploying missile systems in the region.
The former commander told Interfax that Kaliningrad is the region where Russia plans deploy its Iskander-M tactical missile systems.
The missile system, which consists of two types of missiles-- ballistic and cruise – is capable of destroying targets within a range of up to 500 kilometers.
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