"The Russian president remarked that the sharp escalation of the conflict has placed the country, in effect, on the verge of civil war," the Kremlin said in a statement on telephone talks between Putin and German Chancellor Angela Merkel.
But the leaders both "emphasised the importance" of planned four-way talks on Ukraine today between top diplomats of Russia, the European Union, the United States and Ukraine.
The 20 tanks and armoured personnel carriers sent to Slavyansk were the most forceful response yet by the Western-backed government in Kiev to the pro-Kremlin militants' occupation of state buildings in nearly 10 cities across Ukraine's rust belt.
"They must be warned that if they do not lay down their arms, they will be destroyed," Ukrainian Security Service (SBU) General Vasyl Krutov told a group of reporters tracking the sudden tank movements.
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The economically depressed industrial city of 1,00,000 has effectively been under the control of separatist gunmen since Saturday.
Ukrainian troops were also helicoptered into a military aerodrome at Kramatorsk, south of Slavyansk which the interior ministry said was "liberated" without any casualties.
However pro-Russia activist Oleg Issanka told AFP that the troops had opened fire injuring two people.
The Kremlin statement described the actions of the Ukrainian army in eastern Ukraine as an "anti-constitutional course to use force against peaceful protest actions".