The annual report by UNAids and the World Health Organisation says the region had an estimated 250,000 new infections this year, and the number of people with HIV is expected to reach one million by the end of 2001.
It says about 23,000 people in the region will die of Aids-related diseases by the end of this year.
"HIV incidence is rising faster in this region than anywhere else in the world," the report says.
The report was published ahead of World Aids Day on Saturday.
Gloom
In Russia alone, the number of reported HIV infections this year reached 129,000 cases, and have been doubling annually since 1998.
But the report warns that the actual number of Russians with HIV is thought to be much higher than the reported figures.
Ukraine is singled out as the country with the highest HIV prevalence rate.
The new figures show that 1% of the country's adult population carries the infection.
The report also says that Aids is on the rise in Western Europe, despite availability of expensive anti-retroviral drugs.
It predicts that by the end of this year, an estimated 6,800 people will die of the disease and another 560,000 will become carriers.
Chaos
The UN/WHO study says social and economic turmoil have played a major role in the dramatic increase of HIV cases in Russia and other Eastern European countries.
"Mass unemployment and economic insecurity beset much of the region; social and cultural norms are being increasingly liberalised; and public health services are steadily disintegrating.
"Given the current evidence, a much larger and more generalised epidemic is a real threat," the report says.
It points out that the vast majority of reported HIV infections are related to use of injected drugs, which has increased alarmingly especially among young people.
"An estimated 1% of the population [of the former Soviet countries] is injecting drugs," according to the report
High rates of sexually transmitted infections have also contributed to the spread of HIV within the former Soviet Union.
However, the report praised several Central European countries for their efforts in containing the spread of the disease.
It says well-designed national programmes have helped to stop a potential rise in HIV infections in Poland, the Czech Republic, Hungary and Slovenia.
The new figures show that a "declaration of war" on the disease by the UN in June has yet to have any impact.
The primary goal of the campaign was to prevent new infections - by 25% in 15- to 24-year-olds over the next four years, and by half by 2010.