Officials say the officers were tracking the silver Kia Sportage on East Fordham Road around 6 p.m. Sunday. The car, with New Jersey plates, was reported stolen on Saturday.
The Secret Service says a suspect fired a weapon on the National Mall after being confronted by officers and a bystander was injured.
Gunfire outside a convenience store in Harlem led to an officer-involved shooting on Friday night.
Stephenson King, Jr., was fatally shot by a Boston police officer on March 11.
A man brandishing a knife was shot by police in East Harlem around 1:40 a.m. Monday. He is recovering at a local hospital.
According to police, officers were executing an arrest warrant when the man allegedly reached for a weapon.