"After finishing training in the Rostov region (bordering Ukraine), one of the battalions that took part has already returned to base in the Samara region."
"As they finish the tasks given to the participants in exercises, the other units will also return to their permanent bases," Lavrov said at a news conference with his Kazakh counterpart.
Lavrov said President Vladimir Putin had given the same assurance to German Chancellor Angela Merkel when they last spoke on the phone on Monday.
The Russian defense ministry on March 31 said that it was pulling back a battalion from the Rostov region and that the troops were returning to the Samara region, which is around 950 kilometers (600 miles) from the Ukrainian border.
Lavrov stressed that Russia was free to deploy its troops within its own borders and said that "our Western partners recognize that in a legal sense there is no problem here."
The Russian defense ministry has said that its troops have been deployed to carry out several rounds of training exercises in regions close to Ukraine.
Lavrov accused the new authorities in Kiev and Western powers of exaggerating Russia's military presence on Ukraine's borders.
NATO Secretary General Anders Fogh Rasmussen said Wednesday the buildup that the alliance estimates at 40,000 troops was a "matter of grave concern."
The alliance's troop commander General Philip Breedlove has also said Russian troops are poised to attack within 12 hours and could invade vast portions of Ukrainian territory in three to five days.
But Lavrov called on them to "de-escalate the rhetoric", saying: "I would not blow this topic out of proportion as the current Ukrainian authorities and their Western protectors are trying to do."
He in turn warned NATO that it should not deploy additional permanent forces in the alliance's Eastern European member states according to its agreements with Russia.
NATO said Wednesday it had stepped back from a floated idea to reinforce the alliance's military presence in countries bordering Russia, preferring for now to suspend cooperation with Moscow and give more time to talks.
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