"At 19:35 Moscow time (15:35 GMT), the cargo ship separated from the third-stage booster rockets on schedule," the Russian space agency said in a statement on its website after the Progress M-23M ship blasted off from the Baikonur cosmodrome in Kazakhstan.
The ship carrying 2.5 tonnes of supplies including oxygen, containers of food and water and parcels for the crew is due to dock with the ISS at 01:16 am tomorrow (21:16 GMT Wednesday).
Last month, a Soyuz spaceship carrying two Russian cosmonauts and a NASA astronaut, was unable to follow the fast-track route to the ISS after a technical glitch in approach.
The astronauts were forced to spend two days en route to the ISS.
Russia insisted that the glitch was minor and would not prevent future missions from using the fast-track route to the ISS.
NASA has been wholly reliant on Russia for delivering astronauts to the space station since the US retired its space shuttles.