Arsen Avakov, who reported the fighting in an eastern district of the city on his Facebook page today, said the offencive had entered a decisive stage.
An AP journalist just outside Slovens heard sustained gun and artillery fire and saw plumes of black smoke rising over the city.
Avakov warned residents in Slovyansk and nearby cities of Kramatorsk and Krasny Liman to stay at home.
Ukrainian authorities have repeatedly announced an escalation in armed operations, only to eventually back down. Government forces have in recent days been noticeably reinforced to the north of Slovyansk, however, and deployment of air power over the past week has signalled increased determination.