The disclosure came as investigators continued efforts to determine a motive for Saturday's rampage, which ended when Edelmiro Gonzalez was confronted and shot by an off-duty city police officer who happened to be in the area.
Gonzalez's daughter, Yulisa Robles, said her father was involved in a bitter custody fight with 31-year-old Johanna Gonzalez.
"He was just fed up with the situation," Robles, 30, said.
The officer opened fire after Gonzalez refused an order to drop his weapon, and Gonzalez, 54, later died at a nearby hospital. His 7-year-old son, Adrian, was pronounced dead at the scene.
Johanna Gonzalez and their older son, 11-year-old Edryn, remained in critical but stable condition Sunday at St. Joseph's Hospital in Paterson. Further details on their injuries were not disclosed, and authorities said no updates were expected to be issued Sunday.
Gonzalez was armed with two handguns when he approached his family just before 9 a.m., as his wife was dropping their sons off with her mother before she went to work at a local mall, Humphrey said.
When Gonzalez began firing at the family's sport utility vehicle, the boys tried to run away. But their father chased after them and first shot Adrian in the chest, then ran after his oldest son and shot him in the neck.
Gonzalez then returned to the SUV and chased his wife past a fast food restaurant where the off-duty officer, Lt. Washington Griffin, was in the drive-thru lane to pick up breakfast with his young son. Gonzalez then shot her once in the shoulder.
After hearing gunfire, Griffin got out of his car and identified himself as a police officer, Humphrey said, while his son stayed in the vehicle. The 19-year veteran of the force then told Gonzalez to put down the weapon, but he refused and Griffin fired twice, hitting him in the head and the right femur.
Griffin and his son were not injured, but Gonzalez was taken to St. Joseph's Hospital, where he died a short time later.
Griffin was placed on administrative leave pending an investigation by the Passaic County Prosecutor's Office, a standard procedure in police-involved shootings, Humphrey said.
Dominga Nuez, Gonzalez's girlfriend, said that he did not appear to be angry when he left their home Saturday morning.
She said she was shocked when she learned what had happened.
"I can't believe it still. He wasn't violent, and he loved his kids," Nuez said.
