Updated at 7:30 a.m. ET: Three people, including an infant, were shot dead Monday night before the shooter turned the gun on himself, authorities told NBC New York.
The gunman shot two adults and the infant, then killed himself, based on initial reports from the scene in Bayonne, N.J., Mayor Mark Smith said.
Another adult was also shot and was being treated at Bayonne Medical Center for injuries, he added.
Smith told The New York Times that it "looks like murder-suicide."
He told the paper that two other children who were in the home at the time were not hurt, but were "traumatized."
The Times said that preliminary information suggested that the shooter may have been visiting an ex-wife.
A next-door neighbor told NBC New York that his brother heard fighting coming from the home before the shots were fired.
The brother "saw some suspicious activity through the glass door, he heard some loud voices," said the neighbor, who did not wanted to be named. "He goes back in the house to report a domestic dispute and as he's calling it in, he hears some gunshots."
Smith would only say that there was "some type of dispute in the home," and that it "progressed from there."
He would not immediately discuss the relationship of the shooter to the victims.
The Star-Ledger newspaper reported that the shootings happened about 8 p.m. on Monday. Police responded to a call that shots had been fired and they found a woman with a gunshot wound outside the house, the paper said, citing officials.
The paper said the child who died was a boy, aged about a year to 18 months. He was still alive and was taken to hospital, but died later.
According to the Star-Ledger, a man was spotted at Bayonne Medical Center crouched down, rocking back and forth, sobbing and shouting "no."