The girls are between 8 and 16 years old and were attacked in their home by a 49-year-old man who is believed to be their relative, according to the police in New York.
One of the children managed to sneak away and call the emergency center around 10:15 local time.
When the police arrived at the scene, they repeatedly ordered the man to drop the weapon before firing seven shots at him. He was hit by several shots, according to the police.
The suspected perpetrator and the four children were taken to the hospital. The man's condition is serious. The motive behind the act is being investigated.