Prime Minister Giorgi Kvirikashvili, who was returning yesterday to the Georgian capital Tbilisi from a summit with EU leaders in Brussels, diverted his plane to Batumi upon learning of the fire at the posh 22-storey Leogrand hotel.
He pledged a prompt investigation into the cause of the blaze.
"All those responsible for this tragedy will be punished," he said late yesterday.
Officials today revised down the death toll after initially putting it at 12 people.
More From This Section
The victims -- 10 Georgians and an Iranian -- all died of smoke inhalation, the interior ministry said.
Twenty one people were hospitalised, mostly with carbon monoxide poisoning, and were in a stable condition, it added.
Five Turkish nationals and an Israeli were among those injured, regional health minister Zaal Mikeladze said.
The bodies of eight of the victims -- all of them men -- were found in an elevator, another body in a swimming pool and two more in a gym, Georgia's Interpress news agency reported, citing the victims' relatives.
"The electricity went off and all the doors were automatically blocked. We were trying in vain to break windows to get some fresh air," he was reported as saying.
"Firefighters arrived in a few minutes and we were saved."
Georgian President Giorgi Margvelashvili offered his condolences to the victims' families.
Interior Minister Giorgi Gakharia told journalists that an investigation had been launched into the "breach of fire safety norms" in the hotel which reportedly lacked a fire escape staircase.
Twenty participants of the Miss Georgia beauty contest were staying at the hotel when the fire erupted, said Ia Kitsmarishvili, head of a model agency that sought to organise the event.
"None of them has been injured, they have all been evacuated on time," she said in televised remarks.
The contest, which had been due to be held in Batumi today, was postponed, she added.