Interfax news agency said the miners were located in two groups who were communicating with each other - one made up of 33 miners, the other of 13.
Efforts were underway to bring them all to the surface in a special lift.
The Zapadnaya-Kapitalnaya shaft in the southern Rostov-on-Don region, built more than 60 years ago, was flooded by water from an underground lake on Thursday.
Rescuers managed to pull out 25 miners shortly after the accident. Two were seriously injured.
Early on Saturday teams, using simple drills or bare hands, advanced cautiously to guard against tunnel walls collapsing. Officials said the flow of water into the area had eased somewhat.
Hopes rested on the prospect the miners had scrambled into an air pocket 800 metres beneath the surface in the Zapadnya-Kapitalnaya shaft, built more than 60 years ago.
Russian media said President Vladimir Putin, criticised in the past for not responding swiftly to disasters, had ordered officials to "proceed thoroughly with rescue efforts".
The country’s dilapidated and unprofitable network of coal mines has long been subject to accidents. Some collieries date from Josef Stalin's mass industrialisation drive or even earlier.
The television station NTV said industry officials had complained that lack of financing in closing down sections of collieries allowed accumulations of water in shafts taken out of service.
The stricken mine had flooded earlier this year as underground waters rose. No one was working in the shafts at the time.
With the operation underway,
weeping relatives, mainly women and children, milled about the entrance.
Angry relatives of trapped miners
await news of the rescue operation
"This is how Russia loses its men. Men are like rubbish, litter," said Alexander, a miner in his thirties, standing by the shaft.
Others said they had not received their wages for six months.
In neighbouring ex-Soviet Ukraine, more than 200 miners were killed in accidents in each of the last two years.
In June, 11 workers died when a mineshaft collapsed in Russia's Kuzbass field in Siberia. And in post-Soviet Russia's worst such disaster, more than 60 miners died when a methane explosion ripped through a Siberian pit in December 1997.