The Soyuz MS-27 spacecraft was carrying Russians Sergey Ryzhikov and Alexey Zubritsky and NASA astronaut Jonathan Kim.
The trio are scheduled to spend about eight months at the space outpost.
NASA said Kim will conduct scientific investigations and technology demonstrations to help prepare the crew for future space missions and provide benefits to people on Earth. A native of Los Angeles, Kim is a US Navy lieutenant commander and dual-designated naval aviator and flight surgeon.
Russian President Vladimir Putin's investment envoy hailed Tuesday's launch.
"Russian and US co-operation in the space industry continues today," Kirill Dmitriev said, posting a video on his official Telegram channel of the Soyuz rocket blasting off.
Dmitriev, who is trying to spur a reset in US-Russia ties and held talks in Washington last week, said the launch was the latest example of an enduring relationship which traced its history back to 1975.
That was when the first crewed international space mission carried out jointly by the United States and the Soviet Union saw an Apollo and a Soyuz dock in space.
The mission, which featured the first international handshake in space, was a symbol of Cold War detente.
Despite sweeping US sanctions imposed on Moscow over its war in Ukraine, space is one area where co-operation has continued.
Dmitriev, who has talked up the possibility of joint Russian-US investment in the Arctic and in the development of Russian rare earths, has said Moscow could supply a small nuclear power plant for a mission to Mars planned by billionaire entrepreneur and SpaceX CEO Elon Musk.
However, with the ISS nearing the end of its service life, Russia plans to go it alone with its own space station, for which it plans to launch the first two modules in 2027. It is also expanding its co-operation with China in space exploration.
with AP and DPA
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