The first blast occurred late on Saturday as about 370 people were working underground in the mine in Siberia's Kemerovo region.
Twelve miners were initially killed while 300 others managed to reach the surface, according to Interfax news agency.
Just hours later - after rescuers had entered the mine - a second explosion occurred, trapping both the remaining miners and the rescue workers.
Fear of further explosions caused by high levels of methane gas has hindered rescue efforts.
Operations were put on hold throughout Sunday with officials saying the mine was so dangerous that sending people in would be a virtual death sentence.
More than 500 emergency workers from around the country raced throughout the day to restore ventilation to the mine and rebuild mine shafts so the search for those trapped could resume.
Shoigu said rising water levels in the deep mine were another obstacle, giving rescuers a maximum of 48 hours to reach 13 people trapped in two locations that are being flooded.
The Raspadskaya mine, which is 500 metres deep and has 370km of underground tunnels, produces about eight million tonnes of coal a year, according to the company's website.
Mine explosions and other industrial accidents are relatively common in Russia and other former Soviet republics, and are often blamed on inadequate implementation of safety precautions by companies or by workers.
In December, nine people were killed in an explosion at an iron-ore mine in the Urals Mountains region that was blamed on faulty transportation of explosives.
In 2007, a blast at the Ulankovskaya coal mine, also in Kemerovo, left more than 100 people dead.
The authorities had announced in the aftermath of that blast that all surrounding mines would be checked for safety.