Pro-Russia rebels have been fighting government troops in eastern Ukraine for more than three months, leaving at least 400 dead. Kiev has accused Moscow of supplying the rebels with weapons and smuggling them across the border. Moscow denies this claim.
Ministry spokesman Alexander Lukashevich said today that Russia could invite Ukrainian border guards to patrol the border together at two border posts.
Lukashevich added, however, this would only be possible in case of a cease-fire.
The rebels have several Ukrainian border posts under their control and Ukraine has unsuccessfully demanded them back.