The local miners were digging for gold in shafts up to 100 metres (109 yards) underground when the accident occurred on Monday in Mambasa territory in Orientale Province, said Simon Pierre Bolombo, the provincial head of mines.
He said the collapse had been caused by a landslide, Reuters reports.
"It was deep in the forest, there was a landslide, at least 60 people have been killed," Bolombo told Reuters by telephone from the town of Bunia in northeast Congo.
Congo's minister of mines, Martin Kabwelulu, told Reuters the workers were there illegally and that their shafts were deeper than the 30-metre (32-yard) limit required by the mining code for small-scale mining.
Hundreds of thousands of people in eastern Congo make a living in non-industrial mines, where safety precautions are almost nonexistent and accidents are common.
The area where the mine is situated is currently in the hands of a local rebel group - known as Mai Mai Morgan - which will likely hamper any rescue efforts, Bolombo said.
"(The mine) is controlled by the rebels . There's almost total insecurity, it's difficult for us (to reach)," he added.
Mining companies AngloGold Ashanti and Randgold operate in the region, which is known to be rich in tin and gold, although the accident did not take place on either company's concession, officials said.
Armed groups across eastern Congo use illegal and small-scale mining to help fund their activities, despite international attempts to stamp out so-called "conflict minerals".
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