Philadelphia will deploy more police officers and has called for help from the National Guard as it braces for further unrest after the police killing of a black man armed with a knife, authorities said on Tuesday.

Hundreds of protesters took to Philadelphia’s streets on Monday after a bystander’s video was shared on social media showing two officers shooting 27-year-old Walter Wallace after he did not heed orders to back off and to drop the knife.

Wallace was bipolar and his mental issues were relayed to the officers before the shooting, a lawyer for the family said...