Kyiv has been locked in a conflict with Russian-backed separatists since 2014, and this week Ukrainian officials reported Russian troop movement in annexed Crimea and on the border, near territories controlled by Moscow-backed separatists.
On Thursday, Zelensky's ministers discussed the escalating security situation with Western allies, including U.S. Secretary of Defense Lloyd Austin.
Zelensky said in a statement that "military exercises and possible provocations along the border are traditional Russian games." He accused Moscow of seeking to create "a threatening atmosphere" as Kyiv hopes to resume a cease-fire brokered last year.
The U.S. State Department said it was "absolutely concerned by recent escalations of Russian aggressive and provocative actions in eastern Ukraine."
"What we would object to are aggressive actions that have an intent of intimidating, of threatening, our partner Ukraine," State Department spokesman Ned Price told reporters.
Some observers said the reported Russian troop buildup was a test for the administration of U.S. President Joe Biden, who caused an uproar in Moscow last month by calling his Russian counterpart Vladimir Putin a "killer."
This week, Moscow and Kyiv blamed each other for a rise in violence between government forces and Kremlin-backed separatists in eastern Ukraine, which has undermined the cease-fire.
Zelensky said 20 Ukrainian servicemen had been killed and 57 wounded since the start of the year.
Separately, the military announced that a Ukrainian soldier had been wounded in an attack it blamed on separatists.