Seven others were believed buried under the rubble. The Big Gossan underground training facility at the PT Freeport Indonesia mine collapsed last week when 38 workers were undergoing safety training. Ten injured miners were rescued.
A statement from the company said recovery efforts were continuing around the clock.
Indonesian President Susilo Bambang Yudhoyono said he had ordered two Cabinet ministers to personally investigate the accident, but their visits were rejected by the company because rescue efforts were still under way.
"I will continue to order the ministers as well as other concerned officials to thoroughly discuss and investigate to find out what has to be done to ensure safety in the future," Yudhoyono said after presiding over a meeting to discuss the accident. "We will evaluate all mining companies in the country, not only Freeport."
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"I am deeply saddened and disturbed by this event," Adkerson said, adding that "the entire Freeport family around the world joins Freeport Indonesia in grieving for our lost brothers."
The Grasberg mine is one of the world's largest single producers of both copper and gold.
More than 20,000 workers are employed at the mine, which has repeatedly been targeted by arson attacks, roadside bombs and blockades since production began in the 1970s. It is located in the remote mountains of resource-rich but impoverished Papua province, which is home to a decades-long, low-level separatist insurgency.