The man and woman were arrested Thursday in Ecatepec, a violence-hit suburb northeast of Mexico City, on suspicion of killing 10 women.
The man gave detailed accounts of those 10 murders, and told investigators that he and his wife had killed 10 other people as well, according to Gomez.
Prosecutors are now trying to establish whether that is true, or the boast of a "psychopath" and "serial killer," he said.
"He described it in a completely natural way... I would say he actually seemed happy to have done this," Gomez said in an interview with Mexican radio network Formula.
"He wants people to see his picture, to know his name... I would obviously classify this person as a murderer, a serial killer." The couple also admitted to selling the two-month-old baby of one of their victims to another couple, who was also arrested, according to the newspaper El Universal.
He has "a mental disturbance consistent with psychosis and a personality disorder," while she has been "mentally disabled since birth, and also has acquired induced delirium," said Gomez.
He cited a psychiatric exam presented by prosecutors at the man's initial court appearance Sunday.
"But both can distinguish between right and wrong," Gomez added.
The couple were living with their three children, including a baby.
When authorities searched their two houses, they found human remains in cement-filled buckets and wrapped in plastic bags inside a refrigerator, as well as articles of clothing apparently belonging to some of their victims.
The man told investigators that he and his wife lured their victims, many of whom were young mothers, with offers of discount clothing for their babies.
"They were single mothers... and they needed someone who could help them find inexpensive baby clothes," said Gomez.
Investigators tracked down the couple by tracing cell phone calls the missing women had placed to them, he said.
The case has triggered shock in Mexico, even by the standards of a country plagued by a surge in violent crime.
Hundreds of people protested in Ecatepec on Sunday, carrying candles and white flowers to demand action by the authorities to deal with an explosion of violence against women and girls.
Seven women and girls are killed in Mexico every day, according to UN Women. Mexico State, where Ecatepec is located, led the country in femicides last year, with 301 women and girls murdered, according to official figures.
Across Mexico, there were a record 28,702 murders last year. The number has surged since 2006, when the government deployed the army to wage war on the country's violent and powerful drug cartels.
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