NEW YORK — New York City Mayor Bill de Blasio said Wednesday that the death of a 6-year-old boy whose family had been investigated for child abuse “should not have happened.”

De Blasio called Zymere Perkins’ death “an unacceptable tragedy” and added that “the buck stops here.”

Zymere died Sept. 26 after what prosecutors say was months of abuse by his mother and her boyfriend in their Harlem apartment. Both have been arrested on charges of endangering the welfare of a child. Their attorneys did not immediately return calls seeking comment.

City officials have acknowledged that the mother, Geraldine Perkins, was investigated five times for abuse allegations.

The mayor and other officials spoke at City Hall the day after Gladys Carrion, the commissioner of children’s services, said in a tearful television interview that “we can’t keep every child safe.”

Carrion said Wednesday she was “devastated” by Zymere’s death, adding that “the death of one child is too many.”

Five Administration for Children’s Services employees who were involved in the case have been placed on modified assignment during an investigation into the boy’s death.

“We’re looking at every conceivable point along the way where things could have been done differently,” de Blasio said.

De Blasio said the city would institute reforms including improved training for caseworkers.