Expedition 64 NASA astronaut Kate Rubins, left, and Russian cosmonauts Sergey Ryzhikov, center, and Sergey Kud-Sverchkov, right, of Roscosmos are seen as they depart Building 254 to head to their launch onboard the Soyuz MS-17 spacecraft.
Journeys to the ISS usually take around six hours - a time that was a vast improvement on the two-day flights that prevailed prior to 2013.
Only an unmanned Progress cargo space ship has previously used this profile, which requires just two orbits before docking.
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Before May 30, when USA astronauts Robert Behnken and Doug Hurley arrived at the ISS, Russia and Baikonur had enjoyed a lucrative monopoly on manned missions to the ISS.
The launch is sandwiched between two SpaceX missions - the first crewed spaceflights to the ISS under NASA's aegis since 2011.
"We have an incredible partnership", Rubins said in an interview from Russia's Star City before her flight.
She said she was looking forward to scientific experiments planned for the mission.
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The launch also co-incided with Kathleen Rubins' birthday.
Ryzhikov is the commander of flight MS-17 and will take over the command of the ISS from astronaut Chris Cassidy.
Before joining the US space agency, NASA, Rubins worked as a microbiologist and was involved in research on viruses.
This is actually the second spaceflight for Ryzhikov, Rubins, and Kud-Sverchkov and also will make them the 241st people to visit this unique microgravity laboratory. Rogozin on Monday said he didn't conceive Moscow taking an interest "for a huge scope" in a NASA-drove Moon-orbiting station known as The Gateway.
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The Russian space program has endured a progression of switches lately, most prominently the disappointment of a Soyuz rocket in 2018 only minutes after take off - the primary such episode throughout the entire existence of post-Soviet space travel.