"The Troy Police Department is releasing these photos not only for the media but to further appeal to the public for any information regarding this horrific case", Capt. Dan DeWolf of the Troy Police Department said in a statement.
Troy police on Thursday identified the victims as 36-year-old Shanta Myers; her children, 11-year-old Jeremiah Myers and 5-year-old Shanise Myers; and 22-year-old Brandi Mells.
The city of Troy is located just outside of the state capital, Albany, and is about 160 miles north of New York City.
Tedesco did speak about the horrific nature of the murders, saying: "After being in this business for nearly 42 years, I can't describe the savagery of a person like this".
A mother, her girlfriend and two young children were found dead with their throats slashed in their own basement earlier this week.
"There's not a resource we won't tap", Tedesco told reporters.
"I don't have the word."
"Nobody that's been involved in this case is going to ever forget this, I can tell you that", he later told reporters.
Shanta Myers' sister said they had planned to spend the holiday together.
Apparently, there was evidence discovered that suggests the murders were not a random act.
"It feels like somebody ripped us to shreds and we only have each other right now and we are grasping and holding on to each other for dear life". "I can only ask if you know anything at all, even if you think its insignificant, call us".
Myers' sister, Shakera Symes, had implored any potential witnesses to speak with authorities to find "the person who has destroyed us, emotionally, mentally", according to the Times Union.
The childrens' uncle, Khalif Coleman, said 5-year-old Shanise was unusually mature for her age.
"I mean, there was no telling that girl what to do!" Also killed was Myers' partner, Brandi Mells.
"Unfortunately, it's frightful, terrible, sad - especially at this time of the year - that there's four deceased folks in there", he said. "This will be a full-court press until somebody's brought to justice".