The previously reported number was 12 people, with another 30 injured.
"A total of 13 people have died from fire", the emergency service said in a statement.
According to the service, another body was discovered on Wednesday during debris clearance.
Eight fire victims are still in the hospital.
The fire broke out at the Odessa Economics College last week.
President Volodymyr Zelensky instructed the Odessa authorities to do everything to help those affected by the fire and quickly find out how the tragedy occurred. He additionally declared 8 December a national day of mourning.