The trio was due to arrive at the station about six hours after liftoff.
NASA astronaut Anne McClain will join Russia's Oleg Kononenko and David Saint-Jacques from the Canadian Space Agency aboard a Soyuz MS-11 spacecraft set to blast off from the Baikonur Cosmodrome in Kazakhstan at 3:31 a.m. PT.
Speaking before the trip on Sunday, crew commander Oleg Kononenko affirmed his crew "absolutely" trusted the flight's preparation.
Canadian astronaut David Saint-Jacques blasts off on Russian rocket
"We are psychologically and technically prepared for blastoff and any situation which, God forbid, may occur on board", the 54-year-old said.
NASA and Roscosmos said that all onboard systems were operating normally and the crew was feeling fine.
Canada's Saint-Jacques, 48, described the Soyuz spacecraft as "incredibly safe".
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The mission marked the 100th orbital launch of 2018, and the first time in 28 years that humanity reached that number of launches within a calendar year.
The launch was the first for the Soviet-era Soyuz since October 11, when a rocket carrying Russia's Aleksey Ovchinin and USA astronaut Nick Hague failed just minutes after blast-off, forcing the pair to make an emergency landing. The pair landed safely about 12 miles east of the city of Dzhezkazgan in Kazakhstan.
They escaped unharmed but the failed launch - the first such incident in Russia's post-Soviet history - raised concerns about the state of the Soyuz programme.
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In a photo provided by Roscosmos, NASA Astronaut Nick Hague, left, and Roscosmos cosmonaut Alexei Ovchinin after an emergency landing following the failure of a Russian booster rocket carrying them to the International Space Station, in Baikonur, Kazakhstan.
Last month Roscosmos, Russia's space agency, said it had taken measures to prevent the problem from happening again and NASA administrator Jim Bridenstine said he was confident the next ISS crew would fly in a Soyuz in December.
The FSB reportedly intervened to demand the cancellation of the contract between USA firm OneWeb and state corporation Roscosmos to launch a constellation of internet-connectivity satellites.
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