"This will be followed by an adequate response and everyone who has any fault in this tragedy, will be punished", Kvirikashvili said.
Local media reported that the conflagration had allegedly started in the spa of the 22-storey Leogrand hotel when it was used by Miss Georgia beauty pageant contestants.
Twelve people died in fire in the Leogrand hotel in Georgia's Black Sea resort city of Batumi, the Georgian interior ministry said late on Friday.
Earlier on in the day, Georgian Deputy Health Minister Zaza Sopromadze said 21 people had been taken to hospitals, three were promptly discharged.
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"Ten people were hospitalized, mostly with smoke inhalation injuries".
Formal identification of the victims is said to be under way, but an interior ministry statement said one Iranian and 10 Georgians were killed in the blaze.
Leogrand Hotel is now hosting this year's Miss Georgia contest, but organizers said none of the contestants were injured in fire. Georgian President Giorgi Margvelashvili offered his condolences to the victims' families.
"None of them has been injured, they have all been evacuated on time", she said in televised remarks.