Police arrested the 39-year-old father, Juan Rodriguez.
The father of the children went to work at 8 a.m. Friday and forgot the babies in the vehicle, according to FDNY officials.
"I blanked out. My babies are dead".
Mariza and Phoenix Rodriguez were around 1 year old when they died, according to NYPD sources, CBSNewYork reported.
"Certainly it's unimaginable, and at the time that I had occasion to speak to my client last night ... he was inconsolable", his lawyer, Joey Jackson, said in court.
Rodriguez's wife spoke out about her husband and the incident in a statement shared to PEOPLE by Jackson. "I killed my babies", prosecutors said Saturday.
The New York Post reports they were dead and "foaming at the mouth", and Rodriguez began screaming. "I will never get over this loss and I know he will never forgive himself for this mistake".
"Luna and Phoenix will always live in our hearts and memories and we are working hard to come to terms with what has happened. As matter of respect to the family during this hard time, and with due regard to their privacy, we have no further comment at this time".
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Rodriguez, 39, is alleged to have parked up at around 8am before work.
"He carried on with his day", Assistant District Attorney Jaime Breslin told the judge, according to The Post.
Police say when Rodriguez, who is a social worker, discovered the children dead in the backseat of his auto hours later, he said, "I blanked out".
"I assumed I dropped them off at daycare before I went to work", Rodriguez told officers who arrived on the scene, according to court documents.
The Office of the Chief Medical Examiner found the body temperature of both children was 108 degrees Fahrenheit, per the court document.
The New York Police Department said in a news release the boy and girl were found Friday unconscious and unresponsive in the back seat of a Honda sedan in the Bronx.
The boy and girl were pronounced tiresome on the scene.
A Hudson Valley man and father of infant twins he allegedly forgot inside a hot auto while at work has been charged in their deaths, police said.