The Soyuz rocket set off from Kazakhstan at 02:40 GMT on Sunday with Russian, Japanese and American astronauts on board.
They are set to dock with the ISS, a $100 billion research complex orbiting around 385 km (240 miles) above Earth, early on Tuesday.
NASA said the Soyuz TMA-05M rocket had a “smooth ride into space”.
The astronauts on board, veteran Russian cosmonaut Yuri Malenchenko, NASA’s Sunitia Williams and Japanese astronaut Akihiko Hoshide will join three others on board the ISS.
NASA flight engineer Joseph Acaba and Russian cosmonauts Gennady Padalka and Sergei Revin are already living aboard the space station, which is set to receive an unprecedented level of traffic over the next few weeks.
According to the Associated Press news agency, a Japanese cargo ship will dock with the station next week, followed by a further eight craft making contact with the orbiting satellite.
NASA ended its space shuttle programme in July 2011, and since then US astronauts have depended on Russian Soyuz flights for transport to reach the International Space Station.
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