The family was discovered after a relative went to the home in Abington, Plymouth County, to help get the three children to school Monday morning, District Attorney Tim Cruz said. The relative called 911 around 7:30 a.m.
"The person found an individual bleeding, laying in a position on the couch in the downstairs area and they called the police," he said.
Family members were identified as: 40-year-old Deirdre Zaccardi, 43-year-old Joseph Zaccardi, 11-year-old Alexis Zaccardi and 9-year-old twins Nathaniel and Kathryn Zaccardi, according to the district attorney's office.
Deirdre Zaccardi worked at EMI Strategic Marketing, a Boston advertising agency, for nearly 20 years, according to the company.
"EMI is deeply saddened by the loss of our longtime colleague and friend, Deirdre Zaccardi," the company said in a statement. "A ready smile, optimism in the face of the most daunting of projects, a raft of recipes for her beloved holiday Cookie Swap, a happy story about one or all of her three children -- these memories and more will remain."
"She brought kindness, friendship, caring and a can-do spirit to our community," the company said. "May we all honor her memory by embracing those values every day."
Cruz said, "This is just a horrible, horrible event here for the town of Abington and for the children and the schools."
The three children attended public schools in Abington, which is about 25 miles south of Boston.
"Their presence touched so many lives and there are no words to express the sadness we feel," Superintendent Peter Schafer said in a statement. "Counselors are and will be available throughout the district to help our students during and after school. "
"This is an incredibly terrible event," Cruz said. "It's a crime. ... A crime occurred in that building and three little children are gone forever as a result of this. ... There's not a lot of answers to a heck of a lot of questions."
Cruz said the shootings appear to be an isolated incident.
Authorities said they were not aware of any ongoing domestic issues in the home.
"There was no indication whatsoever and no previous calls that would certainly indicate any type of an issue going on at that household," Abington Police Chief David Majenski said during the news conference.
The deaths were the result of gunshot wounds, according to a preliminary investigation, he said. A medical examiner will determine the official manner and cause of death. Cruz said he expected police to find the weapon or weapons involved.