"Unfortunately, there's a great many such appeals coming from the Eastern Ukrainian regions addressed directly to Putin to intervene in this or that form," spokesman Dmitry Peskov said. "The president is watching the developments in Eastern Ukraine with great concern."
Also in Slaviansk, about 150 km (90 miles) from the Russian border, a small airfield which was occupied by Ukrainian air force planes on Sunday was empty on Monday and pro-separatist forces said they were now in control of it.
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In the town of Horlivka, meanwhile, about 100 pro-Russian separatists attacked the police headquarters. Video footage on Ukrainian television showed an ambulance treating people apparently injured in the attack.
In all, separatists have seized government buildings and security facilities in 10 cities, adding to a growing sense that Ukraine's industrial heartland is slipping out of its grip.
Angered by the death of a state security officer and the wounding of two comrades near Slaviansk, Turchinov warned rebels that an anti-terrorist operation involving the army would begin unless they laid down their arms.
Russia's foreign ministry called the planned military operation a "criminal order" and said the West should bring its allies in Ukraine's government under control.
Outside the Slaviansk city council offices stood a group of about 12 armed men in matching camouflage fatigues with black masks, one of whom was holding a Russian flag.
They said they were Cossacks - paramilitary fighters descended from Tsarist-era border patrolmen - but did not say where from. One told Reuters: "The borders between Ukraine, Russia and Belarus are artificial and we are here to take them away."
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The new element in the operation announced by Turchinov is the inclusion of the army which until now had not been involved in more than four months of turmoil and is untested in dealing with internal disorder. The plan implies a lack of confidence in the 30,000-strong interior ministry troops, partly discredited by identification with ousted president Viktor Yanukovich.
The defense ministry on Monday remained silent and would not comment on the army's role.
Turchinov said the Kiev leadership was "not against" a nationwide referendum being held on the type of state Ukraine should be, adding he was sure it would confirm the wish of the majority for a united, independent country.
Russian Foreign Minister Sergei Lavrov said Ukraine's Russian-speaking eastern regions should be involved in drafting a constitution that should be put to a referendum.