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After around 114 seconds of flight, the emergency escape system sprang into action, separating the crew capsule from the rocket.
The launch lifted off from Baikonur Cosmodrome in Kazakhstan at 4:40 a.m. ET, but just six minutes after launch, Roscosmos reported that there was an issue with the booster, as reported by Loren Grush at The Verge.
The Soyuz capsule carrying them separated from the malfunctioning rocket and made what is called a steep ballistic descent with parachutes helping slow its speed.
Rescue crews are now heading towards the emergency landing site in the barren Kazakh steppe to provide support for the crew.
That would, in theory, push the time limit of crew's return to Earth to early January 2019, which is the sole limiting factor, said Dr John Logsdon, head of the Space Policy Institute at The George Washington University.
A tweet from Roscosmos shows the two astronauts resting comfortably, and looking like they're in good spirits, despite what must have been a hard experience.
Footage from inside the Soyuz showed the two men being shaken around at the moment the failure occurred, with their arms and legs flailing.
The astronauts were to dock at the International Space Station six hours after the launch and join an American, a Russian and a German now aboard the station.
In 2003, when Expedition 6 crew members Ken Bowersox and Don Pettit and their cosmonaut counterpart Nikolai Budarin returned from a five-month stay aboard the ISS, their automated controls failed, forcing the re-entry in ballistic mode.
Kremlin spokesman Dmitry Peskov said he expected Russian President Vladimir Putin would be briefed on the incident.
It is not clear how long the Soyuz vehicle will be grounded, or how long the current crew can remain in orbit.
The Russian Soyuz spacecraft is now the only vehicle for ferrying crews to the space station following the retirement of the US space shuttle fleet. "Everybody is alive", Rogozin wrote.
But the Soyuz capsule destined for Saint-Jacques's trip in December is now being assembled, Thirsk said - and if that vehicle is similarly affected to the one that failed on Thursday, "then no, we aren't going to launch in two months. The crew has been saved".
The crew already on the ISS will not be affected by Thursday's aborted mission, Russia's Tass news agency reported, quoting an unnamed source as saying they have enough supplies.
The next re-supply run was meant to happen on October 31, the source was quoted as saying, but that was now in doubt since the Progress supply ship was propelled by the same kind of rocket used in Thursday's incident.