On Wednesday, Moscow rejected the Ukrainian government's claim that a massive Russian military buildup near the countries' border was raising the threat of a possible invasion.
But on Thursday Russia's Defense Ministry announced that thousands of Russian troops in the regions of Rostov, Belgorod, Kursk and Tambov bordering Ukraine are involved in the exercises, which will continue until the end of the month.
In the southern Rostov region, the maneuvers involved parachuting in 1,500 troops, the ministry said. The drills included the military conducting large artillery exercises involving 8,500 soldiers and artillery and rocket systems in the south.
During the Ukrainian crisis, the US has sent additional fighter jets to Poland and Lithuania. Russian responded on Thursday by deploying six fighter jets to Belarus, its ally.
Ukraine's parliament voted Thursday to create a 60,000-strong National Guard to help protect the country as its under-staffed and under-funded military was in disarray.
In New York on Thursday, Ukrainian Prime Minister Arseniy Yatsenyuk condemned Russia's "military aggression," but told the U.N. Security Council he doesn't believe Moscow wants a conflict. "If we start real talks with Russia, I believe we can be real partners," he said.
Putin, who has received his parliament's permission to use the Russian military in Ukraine, has warned that he reserves the right to "use all means" to protect Russian speakers in Ukraine from violent nationalists, even though there have been no signs they are facing such a threat.