"Any type of activity in the forcible intensification [of the situation], of course, will not be in anyone's interest. This topic obviously in of itself will hardly provide for an increase in the level of mutual trust or the balance of interests on the European continent," Peskov told journalists.
Peskov added that the Kremlin is following the rumors that Washington may deploy nuclear weapons in the United Kingdom.
The development and deployment of nuclear and conventional ground-launched intermediate range ballistic and cruise missiles was banned by the Intermediate-Range Nuclear Forces (INF) Treaty, signed by the United states and the Soviet Union in 1987.
Both the United States and Russia have repeatedly accused each other of violating the Cold War-era agreement.
Violence in eastern Ukraine escalated last week prompting fears that the ceasefire between Kiev and independence supporters signed in Minsk in February had broken down. Ukrainian officials publicly acknowledged that Kiev used heavy artillery in recent fighting, in violation of the Minsk peace accords.
The Western leaders accuse Russia of escalating the internal conflict in eastern Ukraine, a claim Moscow has firmly denied.