American Nick Hague and Russian Aleksey Ovchinin were forced to return to Earth and landed in Kazakhstan when the booster stopped working during stage-one separation on their Soyuz rocket at approximately 50km (164,000ft) above the Earth.
"Rescue forces are in communication with Nick Hague and Alexei Ovchinin and we are hearing that they are in good condition", NASA TV said.
The US space agency Nasa said there was an "issue with the booster".
In statements by both Russian Federation and NASA the crew is said to be in "good condition", and no serious injuries have been reported. We await further word from the search and rescue team. Search and rescue teams were immediately scrambled to recover the crew, and paratroopers were dropped from a plane to reach the site quickly.
The rocket took off from Kazakhstan and was on its way to the International Space Station. But the landing engines and parachute system are said to have done their job as normal, getting them back alive to Earth. NASA tentatively plans to send its first crew to the ISS using a SpaceX craft instead of a Soyuz next April. Roscosmos, the Russian firm that operates the nation's space agency and is responsible for Soyuz launches, will not hold any news conferences today. Everything had been going quite smoothly for Roscosmos ahead of the freakish hole discovered in one of their Soyuz spacecraft which was (and still is) attached to the International Space Station.
The failure is the latest mishap for the Russian space programme, which has been dogged by a string of launch failures and other incidents.
Kremlin spokesman Dmitry Peskov said he expected Russian President Vladimir Putin would be briefed on the incident.
It was the first space mission for Hague, who joined NASA's astronaut corps in 2013.
Dzhezkazgan is about 450 kilometers (280 miles) northeast of Baikonur, and spacecraft returning from the ISS normally land in that region. They're scheduled to ride a Soyuz that's docked to the station back down to Kazakhstan in December, but that departure date may now be up for discussion. The space station has enough food and supplies for the current crew to last six months, the Interfax news service reported, citing an unidentified person. "The ISS crew members now in-orbit have been notified of the launch contingency".