Story highlights The father is a CNBC executive, officials familiar with the investigation say.

The nanny was next to the kids with what appeared to be self-inflicted stab wounds, police say

She's in critical but stable condition, the city's police commissioner says

The slain children were 1 and 6 years old

A Manhattan mother returned home early Thursday evening to find two of her young children stabbed to death in a bathtub, as their nanny lay bleeding nearby, police said.

The mother, 38, had just returned around 5:30 p.m. to the family apartment on Manhattan's West Side with her 3-year-old daughter, who she had just taken to swimming lessons, police Commissioner Ray Kelly said.

All the lights were out in the residence, so she went downstairs to ask the doorman whether her two other children and their nanny had gone outside. After the doorman said they had not, the mother went back upstairs and started looking around, Kelly said.

Peering into a bathroom, she let out a scream upon finding her 1-year-old son and 6-year-old daughter stabbed to death in the bathtub, according to Kelly.

The children's 50-year-old nanny was on the bathroom floor unconscious and bleeding from what appeared to be self-inflicted stab wounds to her neck, Kelly said. A kitchen knife sat next to her, according to police spokesman Paul Browne.

A neighbor, Sandy Marcus, told CNN that she called 911 after hearing the mother's screams. Another neighbor recalled it was hard to ascertain what was going on since "everybody was screaming."

The children were taken to Roosevelt Hospital and pronounced dead.

The father of the children is Kevin Krim, an executive with CNBC , several officials familiar with the investigation said.

The nanny is at St. Luke's Hospital, also in New York, in critical but stable condition, according to Kelly. No charges have been filed yet in the case, he added.

Klein described the family at the center of the horror as "all-American" and "lovely."

"It's like something you read about in the papers, in some distant country, but never on your floor," she said.