"After being in this business for almost 42 years, I can't describe the savagery of this," Tedesco told reporters.
"Nobody that's been involved in this case is going to ever forget this, I can tell you that," he added.
Tedesco declined to provide information on how or why the victims were killed.
He said police hoped details will become clear after the autopsies are conducted Wednesday, but provided no details as of Thursday.
The Troy City School District, where the two children attended classes, will be offering grief counseling to students, Superintendent John Carmello said in a statement to the Times Union.
"Our hearts are broken and our thoughts and deepest condolences are with their family and loved ones during this terribly troubling time," Carmello wrote.
The apartment building's property manager discovered the bodies Tuesday afternoon, after the victims' family members told him they were not answering phone calls.
Police responded to the building on Second Avenue in Troy, a city eight miles northeast of Albany, at about 12.50p.m.
Tedesco said it is likely that the family was targeted.
"I don't think there's any doubt that someone who committed a crime of this magnitude is capable of anything," he said.
"But we do not believe this was a random act, and we don't believe there's any imminent danger to the community."
But Jackie Robinson Sr, a pastor at Oak Grove Baptist Church in Troy, told the Albany Times Union that there are "certainly reasons to be fearful".
"We don't know who did it," Robinson said. "Until we find out, it certainly makes sense to be vigilant and keep your doors locked."
The building is in the city's Lansingburgh neighborhood, which runs along the Hudson. Residents told the Albany Times Union that the neighborhood is mostly quiet.
One neighbor, Shakeria Jones, lives around the corner and was worried Tuesday that one of the victims was her friend. But she can't imagine why anyone would kill her, she said, as her friend has not had any problems with anyone, she told the Times Union.
"She lives in the basement apartment," said Jones. "I've been calling her all day. She always answers, but she hasn't. I'm worried it's her. I hope it's not her."
Jason Fenton has lived across the street from the building for 18 years and said that there are four or five apartments in the building. He didn't know its residents but said several children lived there. It seemed like a fun place, he said, with lots of parties during the summer.
The discovery of the bodies, however, is concerning, he said.
"It's horrible," he told the Times-Union. "I hope they find the person."
