Kyiv had earlier accused Moscow of building up military forces near their shared border, and saying that pro-Russian separatists were violating a ceasefire.
Russian Federation is reportedly moving tanks, artillery, and other heavy armored vehicles close to the border with Ukraine, raising fears of an imminent conflict in the region.
While Kremlin spokesman Dmitry Peskov did not directly confirm a troop buildup on the Ukrainian border, he stressed on Thursday that Moscow is at liberty to move troops across its territory.
He declined to specify which measures would be adopted, while insisting that Russian Federation was not making moves to threaten Ukraine.
US Defense Secretary Lloyd Austin spoke with his Ukrainian counterpart, Andrii Taran, and "condemned recent escalations of Russian aggressive and provocative actions in eastern Ukraine", the Pentagon said.
"Russian President Putin said (this) not long ago, but this statement is still relevant today, that those who would try to start a new war in Donbass - will destroy Ukraine".
"There is increased activity on the perimeter of Russia's borders by North Atlantic Treaty Organisation, other alliances, individual countries - it all obliges us to be vigilant", said Peskov.
More than 50 battalion combat teams comprising 15,000 people will take part in those exercises and practice "interaction with electronic warfare and air defense units", the defense military told reporters.
A Ukrainian serviceman changes his position near the line of contact near Vodiane, about 750 kilometers (468 miles) south-east of Kyiv, eastern Ukraine, March 5, 2021.
According to the last reports, the United States government said it was trying to figure out with Moscow whether it was renewing its offensive in eastern Ukraine with 4,000 troops on the move or simply exercising.
Despite several different videos showing trains full of armored vehicles streaming toward the border, Moscow is insisting that it is not sending troops to reinforce the separatists in the Donbass.
Despite an EU-brokered ceasefire known as the Minsk Protocol that came into force in 2015, there have been repeated bouts of conflict since, as the two sides face off across a 500-kilometer frontline dividing the disputed territory between Ukrainian forces and the Russia-backed separatists.
US President Joe Biden and Ukrainian President Volodymyr Zelenskyy had their first phone conversation as counterparts on Friday, the White House said in a statement.
According to Gen Khomchak, Russia also has almost 3,000 officers and military instructors in the rebel units in eastern Ukraine.
There are also reports of increased Russian aggression on the border with Ukraine with multiple deaths reported last week.
Russian tanks T-72 B3 roll through Red Square during the Victory Day military parade in downtown Moscow on May 9, 2019.
Together with France, Germany and Ukraine, Russia is part of the Normandy format of countries that have sought to resolve the conflict and in 2015 agreed the Minsk accords to reduce the fighting.
Since 2014, the United States has committed more than $2 billion in security assistance to Ukraine, including a recently announced $125 million package that featured defensive weapons and other key capabilities to enhance the lethality, command and control, and situational awareness of Ukraine's Armed Forces.