The bodies were discovered in their basement apartment in Troy, near Albany, Tuesday afternoon.
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The victims, whose identities have not been released, were two adult women, ages 22 and 36, a 5-year-old girl and an 11-year-old boy. Troy police said the women were in a relationship together, with the two children belonging to one of them.
Police said Wednesday they believe the victims were targeted and that the public is not believed to be in any danger. They stressed this was "not a random act." Investigators are actively seeking a suspect, though they said they're not sure if more than one person was involved in the killings.
"We're talking about the tragic taking of four lives," Troy Police Chief John Tedesco said. "I can only ask if you know anything at all, even if you think its insignificant, call us."
Tedesco told ABC News that these killings were act of "savagery."
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"The emotions of a police officer are something you repress because there is a job to be done," Tedesco said, adding that no one involved in this case will ever forget it.
Law enforcement sources told media outlets in Albany that the victims were all found tied up.
The cause of death and motive for the killings have not been released. Autopsies were being performed on the bodies Wednesday.