" The commander in the area of training and explain the path for troop movement plans to leave the area , " Interfax quoted the ministry source .
"People have started to dismantle their tents , unload equipment and form rows of vehicles and armor , " the ministry said .
Putin on Monday announced that the troops , which is estimated to number 40,000 NATO officer , who will return to the base after the end of spring training .
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Their presence has increased its deep concern in the West after Moscow annexed the Crimea in March and rebellion broke out in eastern Ukraine on the pro - Western authorities who took power after the February ouster of the Kremlin -backed government .
The withdrawal could ease tensions ahead of Ukraine's presidential election Sunday, but both Washington and NATO - who recorded the third time Moscow has made such a claim - say they do not see any signs of its withdrawal .
According to Interfax , the Russian defense minister has ordered the troops back to their bases after military exercises near the border with Ukraine , to meet the orders of President Vladimir Putin .
The Kremlin announced Monday that Putin has ordered Russian troops near Ukraine return to their bases , but NATO and the United States say they do not see any signs of withdrawal . Moscow does not implement such promises before.
The defense ministry said troops , military training involved in the Rostov region , Belgorod and Bryansk ordered to retreat , the report said .
A defense ministry spokesman declined to comment on the developments .
Moscow to hold tens of thousands of troops near the border areas where separatists have announced independent countries , and Kiev and its Western allies worry that they can be used to support the rebel invasion , according to AFP .