Police say officers shot Walter Wallace, 27, when he ignored orders to drop a knife. His family say he was experiencing a mental health crisis.
Hundreds of protesters were back on the streets in West Philadelphia on Tuesday night in a march against police brutality.
It was the second night of protests following the fatal shooting of a Black man by Philadelphia police.
The man, identified by city officials as Walter Wallace, 27, was shot before 4 p.m. Monday in an episode filmed by a bystander and posted on social media.
A lawyer representing Wallace's family called the victim's shooting "unjustified."
The family had called for an ambulance to get him help with a mental health crisis, not for police intervention, the lawyer said on Tuesday.
Police said Wallace was wielding a knife and ignored orders to drop the weapon before officers fired shots on Monday afternoon.
But his parents said Tuesday night that officers knew their son was in a mental health crisis because they had been to the family's house three times on Monday.
The Wallace family's attorney, Shaka Johnson, said the man's wife, Dominique Wallace, is pregnant and is scheduled to have labor induced Wednesday.
Johnson said Wallace had nine children - two briefly spoke at a news conference late Tuesday, along with Walter Wallace's mother and father.
About 500 people had gathered at a West Philadelphia park Tuesday night and began marching through the neighborhood, chanting.
There were sporadic reports of arrests in other areas of the city Tuesday night around 9 p.m.
Video showed people streaming into stores and stealing goods as they left on the opposite side of the city from where Wallace was shot.
The Philadelphia Office of Emergency Management tweeted around 9:30 p.m. Tuesday, cautioning residents in eastern Philadelphia to remain indoors.
Philadelphia officials had anticipated a second night of unrest Tuesday, after Philadelphia police arrested more than 90 people during protests and unrest that began Monday and spread into the early morning hours of Tuesday, sometimes turning into violent confrontations with police.
Police had previously said 30 officers were injured in the unrest, most of them hit with thrown objects like bricks.
On Tuesday police were stationing extra officers on business corridors in west Philadelphia and elsewhere in preparation.