The only confirmed casualties in Slovyansk were among Ukrainian government forces.
Turchynov said a Security Service captain was killed and two colonels were wounded in Sunday's gun battle. An Associated Press reporter saw a bullet-ridden SUV on the side of the road and a pool of blood by the front passenger seat door, where the clash was reported to have occurred.
Turchynov said pro-Russia militiamen were responsible for the attack.
Vladimir Kolodchenko, a lawmaker from the area who said he witnessed the attack, said a car carrying four gunmen pulled up by a wooded area where government troops were standing by several parked armored personnel carriers and other vehicles.
Kolodchenko, who expressed sympathy for the pro-Russian groups, described the attack as a provocation and an attempt to create a pretext for an all-out assault on Slovyansk.
Those leading the storming of government buildings say Russian-speakers rights can only be assured with full autonomy for eastern regions - a move they insist should be endorsed by referendums. A similar vote in Crimea last month resulted in the peninsula splitting off from Ukraine and being annexed by Russia.
In Luhansk - a town of 420,000 across the border from Russia - heavily armed men still control the security services building. In Donetsk, 80 miles to the west, an occupied regional government building is now serving as the headquarters of a self-declared autonomous region billing itself the Donetsk Republic.
All occupations have drawn crowds of sympathizers.
Ukraine's Foreign Ministry issued a statement late Sunday afternoon accusing "the Russian special service and saboteurs" of fomenting unrest and pledging to present "concrete evidence" of Russia's involvement at a summit on Ukraine in Geneva on Thursday.
In a phone call with Russian Foreign Minister Sergey Lavrov late Saturday, U.S. Secretary of State John Kerry "expressed strong concern" that the attacks "were orchestrated and synchronized, similar to previous attacks in eastern Ukraine and Crimea," according the State Department.
The Russian Foreign Ministry denied Kerry's claims, saying Lavrov blamed the crisis in Ukraine on the failure of the Kiev government "to take into account the legitimate needs and interests of the Russian and Russian-speaking population." Lavrov also warned that Russia may pull out of the Ukraine summit if Kiev uses force against "residents of the southeast who were driven to despair."
Two rival rallies in another regional capital in eastern Ukraine, Kharkiv, turned violent on Sunday when a group of pro-Russian protesters followed several pro-Ukrainian activists, beating them with bats and sticks, Interfax Ukraine news agency reported. Interfax quoted Kharkiv authorities as saying 10 people were injured at the rallies.
An attack was also reported on a police station in the nearby city of Kramatorsk. A video from local news website Kramatorsk.info showed a group of camouflaged men armed with automatic weapons storming the building. The website also reported that supporters of the separatist Donetsk Republic occupied the administration building, built a barricade with tires around it and planted a Russian flag nearby.
Regional news website OstroV said three key administrative buildings were seized in another city in the area, Enakiyeve. In Mariupol, a city on the Azov Sea just 30 miles from the Russian border, the city hall was seized by armed masked men. Local news website 0629.com.ua said 1,000 protesters were building a barricade around it, while armed men raised the Russian flag over the building.
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Nataliya Vasilyeva in Kiev, Lynn Berry in Moscow, Maria Sanminiatelli at the United Nations and Stephen Braun in Washington contributed to this report.
