The Soyuz MS-16 spaceship blasted off at 11:05 Moscow time (0805 GMT) from the Baikonur Cosmodrome in Kazakhstan, the Russian state space corporation Roscosmos said.
The crew includes Roscosmos astronauts Anatoly Ivanishin and Ivan Vagner and their NASA colleague Christopher Cassidy, it said in a statement.
Docking of the spacecraft with the ISS is scheduled to take place at 17:15 Moscow time (1415 GMT).
The arrivals will join Roscosmos astronaut Oleg Skripochka and NASA astronauts Andrew Morgan and Jessica Meir on the ISS, who is scheduled to return to Earth on April 16.
The mission of the new crew is expected to last 196 days, during which astronauts will maintain the station’s operability, work on its re-equipping, conduct experiments, and unload manned and cargo ships, Roscosmos said.