Russian troops that were holding military exercises in the regions bordering Ukraine have begun to dismantle their equipment and return to their barracks, according to the Russian Defence Ministry.
The statement comes after Russian President Vladimir Putin allegedly ordered his defence chief to bring Russian troops back to their permanent bases after the military drills in the regions of Belgorod, Bryansk and Rostov.
The ministry said that the regiments had packed their field camps and prepared their military vehicles for exit before "moving toward train stations and airfields" to return to their bases, said the RIA news agency.
However, Nato had still not seen any indication that the Russian troop withdrawal was taking place following the reports.
"We still have not seen any evidence of a Russian withdrawal of troops from the Ukraine border area," a Nato military officer said, speaking on condition of anonymity.
The Russian Defence Ministry did not confirm how many troops would leave the border areas following the exit.
Reports of up to 40,000 troops stationed near the shared Russian-Ukrainian border were previously confirmed by Nato's military chief General Philip Breedlove.
Pentagon spokesman Rear Admiral John Kirby said the US wants to see the "departure of significant numbers of [Russian] troops back to their home bases".
"President Putin said he's ordered them back to their home bases, which to us means a wholesale withdrawal of all the forces that are readied on the Ukrainian border. We have not seen that yet," Kirby said earlier this week.