Yelin said that 22 people were injured during the protest, including 17 police officers and five protesters.
Russia's Ren-TV television channel showed dozens of riot police with shields approaching the protesters, while some young men threw rocks at them. It also showed a woman with a bloody face.
At least 24 people are still missing after methane gas explosions at the Raspadskaya coal mine, Russia's largest undergound coal mine, on May 8.
The search for the missing men was suspended on Thursday because of heavy concentrations of methane and fires in the tunnels.
There have been no reports of any contact being established with the missing miners, who were believed to be about 450 metres underground at the time of the explosions.
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.
Union leaders said that highlighted the dangerous conditions and poor pay of Russian miners.
"It is the fault of the authorities that they pushed people onto the rails," Ivan Mokhnachuk, the head of Russia's independent coal miners union, told Echo of Moscow on Saturday.
"When people are kept in the dark, when their questions are not answered, when they are left alone, when every day there are dozens of funerals and the authorities do not want to talk, a situation arises where people are displeased."
The governor of the Kemerevo region appealed for calm and promised the miners they would be paid while the coal mine remained out of action because of clearing up operations after the disaster.