3:56 PM PT -- O'Reilly is apologizing to Eric, and says "The message I tried to send was that allegations harm kids. Nothing more."

Ex-Fox News Channel anchor Eric Bolling is firing a warning shot to his old co-worker Bill O'Reilly for bringing up his son's death to the New York Times -- the message ... back off.

Bolling released a statement Monday in response to an interview O'Reilly did with the Times over the weekend -- in which the fired FNC host suggested Bolling's son, Eric Jr., was dead because of stories the paper ran about his dad. Eric Sr. doesn't mince words, even for Bill.

Bolling says, "I believe it is beyond inappropriate for anyone to bring in the tragic death of my son Eric Chase Bolling Jr. Just as Bill O'Reilly had wanted to shield his children from the allegations against him, I hope he will honor my request and avoid any future mentions of my son. My parting from Fox News was in no way connected to ... my son's passing."

He goes on to say that the coroner has indicated to him that Eric Jr.'s death was an accident ... and to also take a shot at Bill directly by saying ... "Unlike others who left Fox News amid public allegations and extensive investigations, I parted ways with Fox News in an amicable way and any reference to a firing is flatly wrong."

As we reported ... Eric Jr. died in bed after suffering emotional torture. The coroner has not announced cause of death.