MOSCOW — The authorities in Moscow said on Friday that coronavirus cases are increasing rapidly here and have already pushed the city’s health care system to its limit.

Warning that the outbreak in the Russian capital was far from reaching its peak, Anastasia Rakova, a deputy mayor responsible for health, said that the number of people hospitalized with the illness related to the virus in Moscow had more than doubled over the past week to 6,500. Nearly half of those infected are under the age of 45.

The city’s mayor, Sergei Sobyanin, sounded a further alarm, saying that the virus “is gaining momentum” and that “the situation is becoming increasingly problematic.”

A flurry of bad news on Friday about the outbreak indicated that Russia, relatively spared until now from the ravages of the virus, has started on the same harrowing path taken weeks ago by hard hit countries like Italy and now the United States. This has dashed hopes in the Kremlin that its decision in late January to close Russia’s long border with China, the original source of the virus, and then limit travel from Europe had contained the outbreak.