Interior Minister Arsen Avakov said the "active phase" of the offensive began at dawn and was still raging three hours later.
He said that two Ukrainian soldiers from the part- volunteer National Guard force were wounded in the fighting.
"The terrorists from the Donetsk People's Republic are being headed by a criminal boss known as 'The Chechen,'" Avakov wrote in a Facebook post.
He said the National Guard unit had destroyed a combat patrol vehicle and several rebel sniper positions.
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Rebels who seized about a dozen towns and cities in the industrial region of Donetsk and the neighbouring province of Lugansk in early April have proclaimed independence from Kiev and are seeking to join Kremlin rule.
Well-equipped gunmen from Chechnya - a Muslim Russian republic that fought two post-Soviet wars for independence before falling under Kremlin control - have appeared in growing numbers among the separatists.
Kiev's new leaders and its Western allies accuse the Russian authorities of fomenting the fighting and turning a blind eye to the flow of gunmen and equipment across the border and into eastern Ukraine.
Mariupol witnessed day-long clashes on May 9 that the interior ministry said had claimed 21 lives. Local officials later gave a lower toll.
The two regions have witnessed daily violence that Ukraine's health ministry said had killed 270 civilians and fighters on both sides.
A car blast yesterday in the heart of Donetsk destroyed the minibus of regional separatist Denis Pushilin and killed three of his guards, according to the local government in Donetsk.
Pushilin was not present at the scene of the apparent attack.