"One more man died in hospital over the weekend," the spokeswoman said.
She added that 42 people were still being treated for injuries, with eight of them in a critical condition.
The fire occurred in the afternoon on the fourth floor of the five-story building while the 19-year-old students were having classes.
The flames spread quickly to the fifth floor, cutting students and teachers from exits, forcing them to jump from windows into rescue nets or climb down nearby trees.
A total of six students died on the spot. Three more died later in hospital.
Over the last few years, Russia has seen a number of deadly blazes at schools, universities, hospitals and other public places.
In 2003, over 40 foreign students were killed and 156 injured following a mysterious fire in the student halls at the Peoples' Friendship University of Russia in southwest Moscow.