Russia will have produced two million vaccine doses within the next few days, Putin said.
Russian Health Minister Mikhail Murashko on Wednesday said more than 100,000 people had already been vaccinated against COVID-19, as Moscow presented its Sputnik V vaccine to the United Nations over video link.
President Vladimir Putin earlier ordered authorities to begin mass voluntary vaccinations next week. Russia will have produced two million vaccine doses within the next few days, Putin said.
Russia said last month that its Sputnik V jab was 92% effective at protecting people from COVID-19 according to interim results.
"Let's agree on this - you will not report to me next week, but you will start mass vaccination...let's get to work already," Putin told Deputy Prime Minister Tatiana Golikova.
Golikova said large-scale vaccination could begin on a voluntary basis in December.
The rise in infections has slowed since reaching a high on November 27, with 25,345 new cases reported on Wednesday.
Russia has resisted imposing lockdowns during the second wave of the virus, preferring targeted regional curbs.
With 2,347,401 infections, Russia has the fourth-largest number of COVID-19 cases in the world behind the United States, India and Brazil. It has recorded 41,053 deaths related to COVID-19 since the start of the pandemic.
The Kremlin earlier gave assurances that Russians were first in line to be vaccinated, with Moscow also discussing supply deals with other countries.
"The absolute priority are Russians," Kremlin spokesman Dmitry Peskov said. "Production within Russia, which is already being developed, will meet the needs of Russians."
Authorities in St Petersburg, which reported 3,684 new infections on Wednesday, ordered bars and restaurants to close from December 30 until January 3, to combat the rise in cases there, the RIA news agency reported.
Museums, theatres and concert halls would be closed to the public in the city of more than 5 million people for the duration of Russia's New Year holidays, from December 30 to January 10.
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