The Russian military has said that the troops have returned to their permanent bases after participating in "months-long drills" near the border.
"A stage of combat coordination of divisions, combat crews, squads at motorized units ... has been completed. More than 10,000 military servicemen ... will march to their permanent deployment from the territory of the combined arms' area of drills," Interfax quoted the army as saying.
Western nations worried for the past few months over the troop buildup, which totaled around 100,000 troops at its peak in November. Some nations started to caution that Russia might be in the middle of preparing to invade the Ukraine in a similar fashion to its annexation of Crimea in 2014.
Putin has repeatedly denied such plans, instead claiming the U.S. and its European allies had instead tried to whip up fears of invasion in order to justify their own troop movements on the other side of the border.
Putin urged the Western nations to make pledges to limit expansion and activities ahead of the longer discussions he will engage in with President Biden in January.
"You must give us guarantees, and immediately – now," he said regarding a proposal Russia handed to the United States this month in a move to defuse tensions over Ukraine.
Putin claimed the U.S. had responded positively to the security proposal and said he was hopeful about negotiations next year in Geneva, Reuters reported.
"We are also prepared to discuss them [security guarantees] on the OSCE [Organization for Security and Co-operation in Europe] platform. I hope this initial positive response and the announcement that this work could possibly start in the near future, during the first days of January, would enable us to move ahead," Putin said.