The New Jersey Attorney General's office is investigating the fatal shooting of a man who family and authorities say was mentally ill, after police said he lunged at them with a knife.

Andrew Jerome Washington was fatally shot by Jersey City police officers on Sunday, Jersey City Mayor Steve Fulop said during a news conference Monday.

The original call to emergency responders went to emergency medical services personnel, the mayor said, who then requested assistance from the police department.

"The call came to the police department from the Jersey City medical center that was already on the scene, and they felt it was unsafe to enter or to engage with Mr. Washington directly at that time," Fulop said.

Police were speaking to Washington through the door before they entered, and he was saying things that were "very erratic," the mayor said.

Police spoke with him while outside his residence for close to an hour, according to the mayor, then opened the door to his apartment.

"They entered and they were charged by Mr. Washington with a knife in hand, and they used force, deploying both a firearm and a taser," Fulop said.

The knife Washington held appeared to be a 6- to 8-inch kitchen knife, according to James Shea, the director of public safety for Jersey City.

Washington's family has publicly questioned the police response.

"Why did they bust in there like he was a criminal, like he was threatening someone? He was in his own place," Washington's aunt, Lisa Mendez, said to CNN affiliate WCBS. "He's bipolar, he has a mental condition... We called the crisis center, because we noticed he wasn't taking his medication, he wasn't acting normal."

"Paramedics came. Instead of calling the crisis center, they called the SWAT team. We said, 'Why? Please, don't hurt him,' and we know it's a mental condition, he's having a mental crisis," Mendez told CBS.

Shea described Washington as "mentally ill."

"Mr. Washington is sick," Shea said. "He is not responsible for his actions. He's not bad -- he's sick. He's ill. He's mentally ill. But that does not make him less dangerous, and that's the problem with these jobs for us."

Shea also described a previous incident where police used force against Washington.

In 2011, Washington was the victim of a shooting and "force had to be used against him," Shea said. During that incident, the city's mobile crisis team also originally responded to the call but "called the police department to the scene because they could not interact safely with him," Shea said.

The New Jersey AG's office has body camera footage of Sunday's incident, the mayor said, and urged the AG to "expedite his review and release the footage as quickly as possible."

"I think when you look at the incident and the circumstances, you'd be hard-pressed to say that the medical center and the Jersey police department could have acted differently in this situation," the mayor said.

The investigation is ongoing, according to the AG's office, which said no other information is available at this time.