KIEV, Ukraine—Antigovernment protesters calling for closer ties with Moscow seized regional government headquarters in two cities in Ukraine's east Sunday in the most serious unrest there in the past month.

Around 200 pro-Russian demonstrators broke into the government building in the industrial city of Donetsk, raising a Russian flag and demanding the local council call a referendum on the industrial region joining Russia. Protesters also seized the regional government building in the eastern city of Kharkiv, but left the...