He said that the gang, which operated in the remote Peruvian jungle, might have been involved in dozens more incidents.
He said that one of the suspects claimed other gangs were also involved in such killings.
The gang allegedly cut off their victims' heads, arms and legs, removed the organs, then suspended the torsos from hooks above candles that warmed the flesh as fat dripped into tubs below.
Police dubbed the gang the "Pishtacos" after a Peruvian myth about men who killed to extract human fat.
Experts sceptical
Mejia said two of the suspects were arrested carrying bottles of liquid human fat and told police it was worth about $15,000 per litre.
The fat was sold to intermediaries in Peru's capital, Lima, and police suspect it was then sold to cosmetic companies in Europe, Mejia said.
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"I can't see why there would be a black market for fat"
Adam Katz, professor at University of Virginia medical school
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He could not confirm any sales.
The group apparently stored the fat in used soda and water bottles, which police showed reporters.
Angel Toldeo, a police commander, said: "We have people detained who have declared and stated how they murdered people with the aim being to extract their fat in rudimentary labs and sell it."
Dr Lisa Donofrio, a dermatology professor at Yale University in the US, was quoted by the Associated Press as saying that a small market may exist for "human fat extracts" to keep skin supple.
But she said that scientifically such treatments are "pure baloney".
The AP also quoted Adam Katz, a professor of plastic surgery at the University of Virginia medical school, as saying: "I can't see why there would be a black market for fat."
Mejia said police received a tip four months ago that human fat from the jungle was being sold in Lima.
Police infiltrated the gang in August, he said, and later obtained some amber fluid, which a police lab confirmed as human fat.