Iran Press/ Europe: Vladimir Putin gave the order during an online meeting with ministers on Wednesday.
Russia has the fourth-highest number of recorded infections in the world and registered 589 new daily deaths from the coronavirus.
Putin said Russia will have produced 2 million vaccine doses within the next few days.
Sputnik V, one of two Russian-made vaccines to have received domestic regulatory approval so far despite clinical trials being incomplete, requires two injections.
Russia said last month that the Sputnik jab was 92% effective at protecting people from COVID-19 according to interim results.
Russia has already vaccinated more than 100,000 high-risk people, Health Minister Mikhail Murashko said during a separate presentation to the United Nations about Sputnik V.
According to the presentation, more than 45,000 people are currently participating in Sputnik V trials worldwide.
The Kremlin earlier gave assurances that Russians were first in line to be vaccinated, with Moscow also discussing supply deals with other countries.
With 2,347,401 infections, Russia only has fewer COVID-19 cases than the United States, India, and Brazil. It has recorded 41,053 deaths related to COVID-19 since the start of the pandemic.
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