The US medical community has rejected Trump's belief that a vaccine could be ready by Election Day.
There are 25 vaccines currently in clinical trials and more than 100 more in development.
But this is not the space race, it's a worldwide pandemic and Putin is trying to claim victory.
Critics say the country's push for a vaccine is partly due to political pressure from the Kremlin.
CNN reports Putin and his team are keen to portray Russia as a global scientific force.
Russia has not released any data on its testing to verify the vaccine's claimed safety or effectiveness.
The New York Times reports Russia has not completed trials.
Despite this, Russia says over 20 countries have expressed interest in the vaccine.
