In the eastern city of Kharkiv, at least 50 people were injured in fighting according to the Interfax news agency.
Video footage shows clashes between supporters of the movement that brought the Kyiv leadership to power and opponents who favour closer ties with Russia.
Eyewitnesses say activists broke into the city council compound and smashed up windows on the ground floor.
In another eastern town, Zaporizhya, scuffles broke out between rival demonstrators. The fighting was captured by on amateur video.
Interfax said 3,000 pro-European supporters turned out in a unity rally, clashing with several hundred pro-Moscow supporters.