Word that the confrontation had ended came a short while after the standoff that had prompted the evacuation of nearby homes entered its third day.
"The Trenton hostage situation is resolved, the three children are safe, and the area is secure," state police Sgt. Adam Grossman told The Associated Press.
In a joint statement with Trenton police and county prosecutors, Grossman indicated that more details will be released at a news conference later in the morning.
He refused to reveal any more about the standoff, including how it ended, what became of the gunman, or any information about the children.
The man, whose identity has not been released, had been holed-up in a two-story red brick house in South Trenton, authorities said. The standoff began Friday afternoon.
During the standoff, police declined to give any details on the number of people being held, their ages or relationship to the armed man.
Earlier, state police Lt. Stephen Jones had described the standoff as an "ongoing, tense situation" and said police were working to "bring this to a peaceful end."
On Saturday, family members of a woman they said was among the hostages grew angry, with some of them going under police tape and briefly confronting officers about the situation.
"Do something! Do something!" screamed a man who said he was the woman's nephew. "Make something happen!"
Police were called to the home before 3 p.m. Friday on reports that a man had barricaded himself inside.
Authorities said police entered the home and found the man brandishing a gun. Police retreated safely, and a SWAT team was called in.
Police said an arson bomb unit was also on the scene. Police declined to say whether the man was making any demands.
Homes on the surrounding block had been evacuated as a precaution, and police tape cordoned off the street in front of the house and nearby. An ambulance was parked near the home but left the scene earlier Saturday.
(Copyright 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.)