They cleared debris blocking the tunnel at Freeport-McMoRan's Grasberg gold and copper mine with saws and wheelbarrows, but cramped conditions prevented them from using heavy earth-moving equipment.
Ten people were hauled out alive during overnight rescue efforts. But those still underground have been trapped for more than 24 hours since the accident early yesterday high in the mountains of rugged Papua province.
The tunnel collapse is just the latest problem to hit the mine, where a major strike in 2011 crippled production.
Police said all 14 were Indonesians.
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"A total of 25 workers are believed to be still trapped in the debris and rescue and recovery work is continuing," said Freeport.
But the company added that rescue efforts by a Freeport team "have been hampered by the confined and restricted space within the tunnel".
Those rescued were taken to a company hospital and were all in a stable condition, said Freeport.
The company previously said 37 people had been trapped when the tunnel collapsed as workers took part in a training exercise, but today revised that figure up to 39.
"This is a very sad day for us," said Freeport Indonesia president Rozik B. Soetjipto.
"Our thoughts and prayers go out to all the victims and their families and we will continue to do our best to evacuate the remaining workers."
Neither Freeport nor police have given any indication of what caused the accident. The firm has said it does not expect the accident to affect production.
It did not disclose the nationalities of all the workers involved in the accident, but the vast majority of the more than 24,000 employees at Grasberg are Indonesian.
The industrial action sparked a wave of deadly clashes between police and gunmen around the mine, with at least 11 people, all Indonesians, killed.
Earlier this month, some 1,100 workers employed by Freeport contractors staged a three-day strike over pay but it caused only minimal disruption to production.