The inmate tried to take his own life on Thanksgiving Day at the jail's George R. Vierno Center with a piece of clothing as the officers looked on before intervening, officials said.
The names of the suspended correction officers were not immediately released.
Brann said the incident, which occurred at about midnight on Nov. 28, was referred to the city's Department of Investigation to conduct an independent inquiry.
The teenage inmate, identified by the city's Legal Aid Society as Nicholas Feliciano, was placed at Rikers Island on Nov. 18 after he was arrested on a parole violation.
The 18-year-old attempted suicide shortly after being removed from the general population after getting into a fight, officials said.
Feliciano was in a medically-induced coma Wednesday in the intensive care unit at Elmhurst Hospital in Queens, according to the Legal Aid Society, which has assigned a defense attorney to represent him.
The Legal Aid Society said Feliciano has a history of mental health problems and suicide attempts.
"Nicholas’ tragedy illustrates the dangers and horrors of relying on our broken parole and correctional systems to address a mental health crisis," the Legal Aid Society said in a statement released on Wednesday. "Despite his young age and known mental health history of past suicide attempts, Nicholas, who is 18 years old, was remanded to New York City jails – a system with a poor track record of managing suicide risks during incarceration – on allegations that have so far resulted in no criminal charges."
The state Department of Correction and Community Supervision canceled the parole warrant and released Feliciano from custody late Wednesday after the Legal Aid Society's Parole Revocation Defense Unit informed the department that "these constraints have already exacerbated his family’s grief and anxiety around this tragedy."
"We are relieved that the New York State Department of Correction and Community Supervision canceled the parole warrant pending against Nicholas Feliciano, our client who is still battling for his life at Elmhurst Hospital in Queens," the Legal Aid Society's statement reads.
"However, this does not abate our concerns over the New York City Department of Correction’s failure to properly screen and address Mr. Feliciano’s mental health issues, which were known to the City at the time of his remand," according to the statement. "Moreover, this tragedy further underscores the need for Albany to enact comprehensive parole reform legislation immediately next session to address cases like Nicholas’, where the alleged violation of parole does not rise to the level of a new criminal charge."
The incident comes about two months after the New York City Council approved a plan to shut down Rikers Island, an 87-year-old, 400-acre lockup in New York City's East River. Rikers is the world's largest jail, housing roughly 7,000 inmates on any given day.
The jail is expected to be shuttered by 2026. Four smaller jails will be built at an estimated cost of $8 billion and be located closer to the city's main courthouses in the boroughs of Manhattan, Brooklyn, the Bronx and Queens.
"Rikers Island is a symbol of brutality and inhumanity and it is time for us to once and for all close Rikers Island," New York City Council Speaker Corey Johnson, a Democrat, said after the council voted to close the jail. "As a city, we must do everything we can to move away from the failed policies of mass incarceration."