Reuters, citing anonymous sources, said Russia’s first potential vaccine would be approved by regulators this month.
However, some experts are concerned at Russia’s fast-track approach.
On Friday, the leading infectious disease expert in the US, Dr Anthony Fauci, said he hoped that Russia – and China – were “actually testing the vaccine” before administering them to anyone.
Dr Fauci has said that the US should have a “safe and effective” vaccine by the end of this year.
“I do not believe that there will be vaccines so far ahead of us that we will have to depend on other countries to get us vaccines,” he told US lawmakers.
Scores of possible coronavirus vaccines are being developed around the world and more than 20 are currently in clinical trials.
Mr Murashko, quoted by Interfax news agency, said that the Gamaleya Institute, a research facility in Moscow, had finished clinical trials of a vaccine and that paperwork was being prepared to register it.
“We plan wider vaccinations for October,” he said, adding that teachers and doctors would be the first to receive it.
Last month, Russian scientists said that early-stage trials of an adenovirus-based vaccine developed by the Gamaleya Institute had been completed and that the results were a success.