The two children were identified as boys but their names have not yet been released.
Their mother, 22, is being held as a “person of interest” but has not been charged, deputy chief Louis De Ceglie said during a news conference late on Saturday.
Police were dispatched to a residence in the Mount Hope area at 7.20pm to a report of a woman acting female acting “erratic, but non-violent, with no weapons”, Mr De Ceglie said.
Officers found a woman naked and acting “irrationally” inside the third floor apartment on Echo Place.
She was taken to St. Barnabas Hospital for evaluation at about 7.50pm, Mr De Ceglie said.
A second 911 call was placed five minutes later to report “two unresponsive babies not breathing at the same location”, Mr De Ceglie said.
The officers returned and located the two boys suffering from multiple stab wounds to their necks and torsos.
The officers attempted CPR and the children were rushed to Columbia Presbyterian Hospital, where they were pronounced dead.
The boys’ father was not in custody, he said.
He said police had been called to one domestic violence incident at the address “a couple of years ago”.
The police officers who responded “were going to have to live with and think about” the incident for the rest of their lives.