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.