"I believe that the goals of the snap check have been fully achieved. The troops have demonstrated their ability to provide a reliable defense of the country. In this regard, I have decided to complete the inspections in the Southern and Western military districts," Defense Minister Sergey Shoigu said in Crimea, the peninsula Moscow annexed from Ukraine in 2014.
Ukrainian President Volodymyr Zelenskyy welcomed the pullback, saying the move "reduces tensions."
"Ukraine is always vigilant, yet welcomes any steps to decrease the military presence and de-escalate the situation in Donbas. Ukraine seeks peace," Zelenskyy wrote on Twitter, adding that he was "grateful to international partners for their support."
Following the pullback announcement, NATO said it would continue to closely monitor the situation.
"Any steps towards de-escalation by Russia would be important and well overdue. NATO remains vigilant," a NATO official said in a statement. "We continue to call on Russia to respect its international commitments and withdraw all its forces from Ukrainian territory."
According to the European Union, about 100,000 troops were at the border.
Moscow, however, has rejected concerns about the buildup, saying it is free to deploy its forces anywhere on Russian territory.
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Russia: Military must be prepared
Shoigu said that the military taking part in the drills should return to their bases by May 1. However, he also ordered that heavy weapons be kept in place about 160 kilometers (100 miles) east of the border for another military exercise later this year.
Shoigu said Russia was watching NATO activity closely, including the military alliance's Defender Europe exercises.
The drills are a new US-led, multinational joint exercise between US and other international forces launched in 2020, and expanded for 2021.
"NATO military activity is significantly increasing in this region," Shoigu said, adding that Russian troops would be on alert in case of "unfavorable development" of the Western exercises.