The clashes broke out a day after masked gunmen stormed a series of police and security service buildings in coordinated raids that Washington's UN envoy Samantha Power said today bore "tell-tale signs of Moscow's involvement".
The heavily Russified region has been riven by unrest since a team of Western-backed leaders rose to power in February on the back of bloody protests against the old regime's decision to reject an EU alliance and look for future assistance from the Kremlin.
Yesrterday's attacks were especially unsettling for both Kiev and Western leaders because of their remarkable similarity to events leading up to Russia's annexation of Ukraine's Crimea peninsula.
The balaclava-clad gunmen were armed with special-issue assault rifles and scopes most often used by nations' crack security troops.
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Many wore unmarked camouflage uniforms similar to those seen on the highly trained units that seized the Black Sea peninsula in early March. They also moved with military precision and cohesion.
"Blood has been spilt in a war that is being waged against Ukraine by Russia," said Turchynov.
"The national security and defence council has decided to launch a full-scale anti-terrorist operation involving the armed forces of Ukraine."
The Russian foreign ministry immediately responded by accusing Ukraine's leaders of "waging war against their own people" and demanding that the UN Security Council immediately address Kiev's use of force.
Moscow has denied playing a role in the latest wave of violence and previously told Kiev that its armed response could ruin the chances of the two sides sitting down for US-EU mediated talks in Geneva on Thursday.