The victims died from inhaling fumes at the 22-storey Leogrand Hotel and Casino on Friday, regional Health Minister Zaal Mikeladze said.
Among those being treated are three Turks and an Israeli, a spokesman for the Batumi University Clinic said.
The cause of fire was not immediately clear but authorities blamed fire regulations for the probable accident.
Prime Minister Giorgi Kvirikashvili and other government officials arrived in Batumi at about midnight. According to officials, no participants of the contest, who were staying at the hotel, were injured in the blaze.
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Participants in the Miss Georgia beauty pageant were among the guests of the hostel at the moment.
The interior ministry earlier said 12 had died, but later adjusted the figure to 11. "The fire has now been extinguished", the regional interior ministry said in a statement.
In a later post he offered his condolences the families and promised an investigation to find the fire's causes.
Survivors told Doğan News Agency (DHA) that the fire erupted in the hotel's boiler room after an explosion, and quickly spread to upper floors.