Sterling Moore, who died at a day-care center in the Labor Department building, had allegedly choked on a meatball. (Family photo)

It was shortly after noon Tuesday when a staffer at the Labor Department day-care center left a message for Jennifer Coleman, an accountant who worked a few floors above in the building on Constitution Avenue.

“Sterling was chewing a meatball and he ended up choking on some of it,” the voice-mail message stated. “Right now we’re trying to get it out but we need you to come down to the school as soon as you can. Thank you.”

By the time Coleman, 26, heard the message and rushed downstairs, her oldest son, ­3-year-old Sterling Moore Jr., was “in an ambulance and was unresponsive,” the child’s grandmother said Wednesday. The grandmother, Cheryl McCarthy of Northeast Washington, forwarded the voice mail to The Washington Post.

D.C. police said Sterling died at Children’s National Medical Center at 12:46 p.m., 39 minutes after the first paramedic was dispatched to the Esther Peterson Child Development Center in the Labor Department building.

Authorities have classified the case as a death investigation and are awaiting results of an autopsy to determine a cause. Police would not comment further on the case.

Officials at the day-care center declined interview requests Wednesday. The center released a statement saying: “We are shocked and deeply saddened as we grieve the sudden death of one of our children. . . . While eating lunch, the child showed difficulty breathing.”

The statement says that staff “responded immediately to call 911 and perform the Heimlich Maneuver and CPR. . . . We are devastated by this tragedy, and our hearts and condolences go out to the family during this unimaginable time of grief.” The statement does not say whether the child choked.

Sterling’s parents, Jennifer Coleman and Sterling Moore Sr., who works in construction, live separately but are planning to live in a house together, the grandmother said. Sterling had a brother who is 7 months old.

McCarthy said the child’s parents are devastated by the death and angry over the tone of the voice mail, which she said masked the urgency of the emergency. “There was no panic in the message at all,” she said.

The grandmother said she and Sterling’s parents are asking why the child was fed a meatball and whether there was sufficient supervision at the time.

“He loved to play with his baby brother,” McCarthy said of her grandson. “He was loving, and he was athletic. At his aunt’s house the other day, we have video of him chasing his little cousin. He was always happy. I don’t understand what happened. I’m just lost.”

McCarthy said her family “wants answers.” She added: “The whole family is in an uproar. He was an innocent child. He was not supposed to go this way.”