"The 63rd Progress resupply ship is beginning its two-day treck to ISS," a NASA commentator said as Russia's Roscosmos space agency aired a live lift-off from its Baikonur launchpad.
The ship went through a flawless ascent to reach space and is expected to dock with one of the modules of the station at 1800 GMT on Saturday, April 2.
The Progress-63 is hauling some three tonnes of food, fuel and supplies to Russian cosmonauts Yuri Malenchenko, Oleg Skripochka and Alexey Ovchinin and NASA astronauts Tim Kopra and Jeff Williams.
Russia is solely responsible for manned flights to the International Space Station, but resupply missions are also carried out by the United States.
On March 26, the Cygnus cargo ship packed with science and research equipment plus food, water and clothes successfully docked at the International Space Station.
Another cargo craft, the SpaceX Dragon, will also dock there on April 10, making it a rare occasion when six spacecraft -- including two Soyuz ships and another Progress ship -- will be attached to the station at the same time.