“Building trust between law enforcement officers and the communities they serve is one of my highest priorities as attorney general,” Ms. Lynch said. “The Department of Justice intends to do everything we can to foster those bonds and create safer and fairer communities across the country.”

Ms. Lynch would not predict how long the investigation might take.

Already, outcry over the case appears to be forcing a change. Under scrutiny over another case — a police shooting that occurred only days before Mr. McDonald’s death — Mr. Emanuel says that the city will now reverse course from its longstanding practice and release police video from that case sometime this week. The video will show the fatal shooting of Ronald Johnson, 25, on Oct. 12, 2014. Chicago police say Mr. Johnson pointed a gun at officers, but a lawyer for his family said that the video will show that he was running away.

The confrontation with Mr. McDonald, who was 17, began after 9 p.m. on Oct. 20, 2014 when he was stopped by the police after a report of someone breaking into vehicles on the Southwest Side. Officers said Mr. McDonald had a three-inch folding knife and ignored calls to drop it. Instead, they said, he walked and jogged away and at one point slashed the tire of a police car.

A growing number of officers followed him for several blocks. A police dashboard camera video, made public on Nov. 24, shows Officer Van Dyke’s police vehicle pulling up just before the shooting began. He fired 16 shots at Mr. McDonald from about 10 feet away, prosecutors have said. No other officer at the scene fired his gun, although at least five corroborated Officer Van Dyke’s version of events — that Mr. McDonald appeared to be coming at them in a threatening way.

After the shooting, the Independent Police Review Authority, a group assigned to review police shootings in Chicago, began investigating. Within two weeks, the city’s information was handed over to prosecutors to conduct their own criminal inquiries.

As lawyers for Mr. McDonald’s mother began looking at the case in late 2014, they say they found puzzling contradictions. Some witnesses disagreed with the police account that Mr. McDonald was coming at Officer Van Dyke. Workers at a nearby Burger King said the police arrived almost immediately after the shooting and began intensely studying a computer that handles the restaurant’s surveillance system.