"The Russian government should immediately withdraw its intelligence and sabotage groups, condemn terrorists and require them to abandon the seized buildings," Yatsenyuk told a cabinet meeting in Kiev.
Describing the movement of pro-Moscow activists in eastern Ukraine as "terrorism," Yatsenyuk said Kiev has evidence that "Russian special services supervise those actions."
Yatsenyuk said that the plea to move Russian forces away from eastern Ukraine would be the main message Kiev would communicate to the international community during the upcoming four-party talks over the crisis in Geneva, Xinhua reported.
The unrest in Ukraine's Russian-speaking east came after Russia absorbed the Ukrainian peninsula of Crimea on March 18 after a referendum.
Pro-Moscow masked men in military uniforms recently seized several government buildings in nearly 10 eastern cities, demanding a referendum on autonomy and closer ties with Russia.
In response to the move, Ukraine launched an "anti-terror" operation, deploying 20 tanks and armored personnel carriers to the eastern region.
To mediate the situation, the European Union, United States, Ukraine and Russia scheduled talks for Thursday to discuss ways to de-escalate the tension.