Ukraine`s military said a pilot and serviceman were killed and nine rebel checkpoints seized.
However, separatists at three Sloviansk checkpoints told the BBC they were still in control there.
Russia says Kiev`s actions "killed the last hope" for a deal agreed last month in Geneva aimed at defusing the crisis.
On Thursday, Russia`s foreign ministry warned that any assaults by Ukraine`s troops in the region would have "catastrophic consequences", triggering fears of an invasion by Moscow.
Sloviansk is a stronghold for pro-Russian separatists who are exerting increasing control in the region.
In a statement on Friday , Ukrainian Interior Minister Arsen Avakov said the "active phase" of the operation began at 04:30 local time.
He said interior troops and the National Guard were involved in the operation in the Sloviansk-Kramatorsk region.
"The terrorists opened fire with heavy weapons against Ukrainian special units.
"A real battle with professional mercenaries is going on," Mr Avakov said, adding that the separatists were using the tactics of hiding behind civilians in residential buildings.
Russia`s state-run Rossiya 24 TV channel said the city was being "stormed".
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