A New York nanny suspected of slaying two young children of a Manhattan couple last month in their luxury apartment has been arrested and charged with murder in their stabbing deaths, New York's deputy police commissioner said.

The nanny, Yoselyn Ortega, was arrested over the deaths of 6-year-old Lucia Krim and her toddler brother Leo, who had been days shy of his second birthday, following a bedside interview at New York Presbyterian Weill Cornell Medical Center.

The children's mother, Marina Krim, found her son and older daughter stabbed to death in the bathtub as she returned home on October 25 from a swimming lesson with a third child, 3-year-old Nessie, who was unharmed, police have said.

The nanny, who remains hospitalised and under guard, then began stabbing herself in front of the children's mother in the apartment on Manhattan's affluent Upper West Side.

"No longer intubated and recuperating from what appeared to be wounds she inflicted on herself at the crime scene, Ortega agreed to talk to New York City detectives this afternoon," Deputy Police Commissioner Paul Browne said in a statement.

"After the interview, at 6:06pm today, Ortega was formally arrested and charged with murdering both children."

He said that Ortega, 50, was charged with two counts of first degree murder and two counts of second degree murder over the killings, which sent shock waves through the city.

Ortega, who had been employed by the Krim family for two years before the killings, lived with her son and sister near the Krims' apartment off Central Park and has been a naturalised US citizen for a decade, police said.

She was apparently referred to the Krims by another family, police have said.

On the evening of the killings, Marina Krim had entered the apartment with her middle child after Ortega failed to meet them as planned at a local dance studio with the two other children.

Krim saw that the apartment was dark and returned to the lobby to ask the doorman if the nanny and kids had gone out, police said. The doorman said no, and she returned to the apartment and went into the bathroom, where she found the children.

Kevin Krim, the children's father and an executive with CNBC, had been heading home from a business trip, He was met by police at the airport and notified of the killings, police said.

- Reuters