Thursday's dramatic launch abort that returned the crew of Soyuz MS-10 safely to Earth after a still-unidentified booster anomaly was the first time a crewed spacecraft bound for the International Space Station has suffered a mission critical failure.
Hague, 43, and Ovchinin, 47, lifted off as scheduled at 2:40 p.m. (0840 GMT; 4:40 a.m. EDT) Thursday from Baikonur.
Russia says it is suspending manned space launches pending a probe into a Russian booster rocket failure, raising questions about the fate of an upcoming launch that included a Canadian astronaut. The contingency procedure sends the spacecraft carrying the crew on a "sharper angle of landing compared to normal", NASA said.
A Reuters reporter who observed the launch from around one kilometre away said it had gone smoothly in its initial stages and that the failure of the booster rockets must have occurred at higher altitude.
The failure is the latest mishap for the Russian space programme, which has been dogged by a string of launch failures and other incidents.
After this morning's launch failed to reach orbit, the International Space Station is left with only three crewmembers aboard, commanded by German astronaut Alexander Gerst.
Search and rescue forces were scrambled from Baikonur Cosmodrome to the expected landing site, a journey of roughly one and a half hours.
The rocket was carrying a Russian cosmonaut and an American astronaut who had set off for a six-month mission at the International Space Station, on a relatively rare two-man launch.
The incident comes as the US has been making progress in its quest to end Russia's monopoly on manned flights to the ISS by encouraging private companies to conduct launches.
Helicopters were able to reach Hague and Ovchinin fairly quickly and get them out of the capsule.
NASA chief Jim Bridenstine said his team is working with their Russian counterparts.
Rogozin was flying to the scene of the emergency landing, the space agency said.
He said all manned launches will be suspended pending an investigation into the cause of the failure. The crew bailed out at an altitude of 164,000 feet and landed safely in Kazakhstan. This is far in excess of what some sources in the Russian press have estimated the crew of Soyuz MS-10 experienced Thursday: anywhere from 5 to 7 Gs.
The crew members of Expedition 57 are conducting experiments in biology, biotechnology, physical science and Earth science aboard the International Space Station.
Rockets use boosters to provide the thrust they need to launch from Earth and breech the atmosphere. In August, a hole appeared in a Soyuz capsule already docked to the ISS that caused a brief loss of air pressure and had to be patched.