Clarkstown police Sgt. Jo Anne Fratianni said Ava Sangavaram was upgraded from critical to stable condition at Westchester Medical Center in Valhalla.
"Eventually the plan is to be able to interview her when she is stable enough," Fratianni said. "We don't know when that will be."
Ava suffered several stab wounds when her mother, podiatrist Victoria Vovchik, tuned on her with a weapon on Thursday at their upscale New City home, about 30 miles from Manhattan, police said. Vovchik then stabbed herself to death, they said.
The Rockland County medical examiner said Vovchik died from two self-inflicted wounds in her neck.
Fratianni wouldn't say if a motive had been detected. She said no note had been found.
The victims were discovered by Ava's father, Kristappa Sangavaram, a New Jersey anesthesiologist. He had been alerted by Ava's school that she was absent, and he went to the home to check on her, Fratianni said.
Sangavaram and Vovchik had never been married, Fratianni said.
He called 911 to report "a possible suicide," police said. He was not being held.
Fratianni would not say exactly what kind of weapon was used in the attack.
"We have evidence we've collected at the scene but we're not able to disclose that," she said.