Putin told U.N. Secretary General Ban Ki-moon that Ukrainian actions in the east were "anti-constitutional." A Kremlin statement quoted him as saying he expected the U.N. and world powers to issue a "clear condemnation" of Kiev.
Turchinov said an offensive he first announced on Sunday was now in progress after days in which it failed to materialize.
"The anti-terrorist operation began during the night in the north of Donetsk region. But it will take place in stages, responsibly, in a considered way," he told parliament. "I stress again: The aim of these operations is to defend the citizens of Ukraine."
At least 15 armoured personnel carriers displaying Ukrainian flags were parked by the side of a road around 50 km (30 miles) north of Slaviansk, witnesses said.
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Ukrainian troops wearing camouflage gear and armed with automatic weapons and grenade-launchers were stationed nearby, with a helicopter and several buses containing interior ministry personnel near the road.
In Slaviansk itself, separatists have seized the local headquarters of the police and state security service.
Outside the police station, about a dozen civilians manned barricades of tyres and wooden crates. A dozen or so armed Cossacks - paramilitary fighters who claim descent from Tsarist-era patrolmen - stood guard at the mayor's offices. Shops were functioning as usual and bread supplies were normal.
In Kiev, a radical, pro-Russian candidate running for Ukrainian presidential elections due next month was beaten up by an angry crowd.
Moscow accuses Kiev of provoking the crisis by ignoring the rights of citizens who use Russian as their first language, and has promised to protect them from attack. Russia also stresses the presence of far-right nationalists among Kiev's new rulers.
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However, a United Nations report on Tuesday cast doubt on whether Russian-speakers were seriously threatened, including those in Crimea who voted to join Russia after Moscow forces had already seized control of the Black Sea peninsula.
"Although there were some attacks against the ethnic Russian community, these were neither systematic nor widespread," said the report by the U.N. human rights office.
Russia called the report one-sided, politicised and apparently fabricated.
NATO Secretary-General Anders Fogh Rasmussen accused Moscow of involvement in the rebellions. "It is very clear that Russia's hand is deeply engaged in this," he told reporters.
Russian Foreign Minister Sergei Lavrov denied that Moscow was stirring up the separatists in the east and southeast as a possible prelude to repeating its annexation of Crimea. "Ukraine is spreading lies that Russia is behind the actions in the southeast," Lavrov said on a visit to China.
Moscow has demanded constitutional change in Ukraine to give more powers to Russian-speaking areas, where most of the country's heavy industry lies, while the rebels have demanded Crimean-style referendums on secession in their regions.