The fire quickly engulfed most of the dilapidated building housing students of the Patrice Lumumba Friendship of Peoples University, said Emergency Situations Ministry spokesman Viktor Beltsov. The building served as a quarantine facility for newly arrived foreign students needing medical checks before starting their studies.
"It was like a horrible nightmare," said Abdallah Bong, a student from Chad, looking at the gutted building. "We saw them crying for help and jumping out of the windows, and we could do nothing to save them."
Pavel Klimovsky, a Moscow police spokesman, said 28 bodies were recovered inside the building, which housed 272 students, three were found outside and one person died in an ambulance. He said 50 of the injured were in serious condition.
Mr Bong and other witnesses said fire engines were slow to start action as they jammed into a narrow access road blocked by parked cars, unable to stop the flames from gutting most of the dormitory above the ground floor.
The fire burned for more than three hours.
Smoke poured from windows as a wet snow fell in the pre-dawn darkness, and, after the fire was put out, the building's concrete walls were streaked with dark black soot. Nearby trees were caked with ice that had formed from water used to extinguish the blaze.
"A friend of mine, who arrived just a few days ago, broke his leg when he jumped out the window, and I don't know what happened to another friend," Nafafe Tengna, a third-year journalism student from Guinea, said as he waited for authorities to distribute a list of victims.
He said firefighters and emergency workers were slow to mount a rescue effort.
"Students had to do it all themselves, holding mattresses for those who were jumping out," he said.
Later, some half-naked victims suffered frostbite waiting for ambulances.
Moscow fire safety department spokesman Yevgeny Bobylyov insisted that the firefighters arrived on time and did their job well.
Rimma Maslova, the chief doctor at a nearby hospital where most of the wounded were being treated, said that many suffered fractures and one had a grave spine injury.
Students said the dead and injured included citizens of China, Bangladesh, Vietnam, Ecuador, Ethiopia, Tahiti, Afghanistan, Tajikistan, Angola, Ivory Coast, Morocco, Kazakhstan, the Dominican Republic, Lebanon, Peru and Malaysia.
A preliminary investigation pointed to an electrical problem, Deputy Interior Minister Rashid Nurgaliyev told Russian President Vladimir Putin, who enquired about the fire during a Cabinet session. Some bystanders said the fire could have been sparked by electric heaters.
The university, named for a Congolese anti-colonial leader and prime minister who was assassinated, was founded by Soviet leader Nikita Khrushchev in 1960 to offer a strict Marxist curriculum to students from developing nations.
It served as a showcase of Soviet patronage of the third world, receiving generous state subsidies, but declined after the 1991 Soviet collapse when government funding dried up.
A 22-year-old student from Mauritius, who identified himself only by his first name, Vashish, said the university charges high prices for "miserable" lodging. He and other students said one of the dormitory's two stairways was permanently locked, making it more difficult to escape.
With stipends shrinking to almost nothing, many foreign students sell goods from their countries to make money, and already cramped dormitories are often packed with bags and bundles.
Russia has a high rate of fire deaths, 18,000 a year. That is nearly five times the number of fire deaths in the United States, which has twice the population. The contrast is even starker with Britain, where there are 600 fire deaths a year, or one per 100,000 people compared to 12.5 per 100,000 in Russia.
Experts say fire fatalities have skyrocketed since the end of the Soviet Union, in part because of lower public vigilance and a disregard for safety standards. The age of Russia's buildings also plays a role: many older buildings have wood partitions between the floors that help fires spread rapidly.