Russia announced last month that its vaccine, named "Sputnik V" after the Soviet-era satellite that was the first launched into space in 1957, had already received approval. 

"The first participants have already had the vaccination at clinics in the capital," Deputy Mayor Anastasia Rakova, responsible for social development, said in a statement.

The vaccine project is financed by Russia's sovereign wealth fund, the Russian Direct Investment Fund.

The vaccine was developed by the Gamaleya research institute in Moscow in coordination with the Russian defense ministry.

High-profile Russians have already been vaccinated, including President Vladimir Putin's daughter, nationalist politician Vladimir Zhirinovsky and Moscow Mayor Sergei Sobyanin.

Putin's spokesman Dmitry Peskov said Wednesday that the president would "inform you about it himself" if he decided to get vaccinated.

The Moscow city government website said 40,000 people from the capital can receive the vaccine, given in two doses with a 21-day interval.

The site says they are taking part in a "post-registration study" of the vaccine.

Those volunteering must not have had COVID-19 or recent contact with anyone ill and must not be pregnant or trying for a baby.

Rakova said that more than 35,000 Muscovites had already applied online.

The Moscow city's website says that volunteers will be closely monitored via a specially created app.

Russia will also make the vaccine available shortly for people in high-risk groups: medics and teachers, who will receive it on a voluntary basis and will also be monitored.

Russia raised concerns among Western scientists by announcing that the vaccine had received approval before full clinical trials has been completed. 

Patients in early trials involving 76 people all developed antibodies, according to research published in The Lancet medical journal last week, while experts said the trials were too small to prove safety and effectiveness.

The phase three trials, which the health ministry said began on Wednesday, are more rigorous and include some volunteers receiving a placebo. These will take part in several countries, according to the vaccine's website. 

Russia has said it is ready to manufacture 500 million doses of vaccine per year.

The country has confirmed more than 1 million coronavirus cases and 18,305 people have died. 

Moscow's infection rate has been relatively stable in recent months with 642 new cases confirmed Wednesday.