Bettie Jones, a 55-year-old grandmother, was enjoying a Christmas celebration the night before she was shot, Jahmal Cole, the husband of Jones' niece, said at a news conference today.
"This is not the time for hatred," Cole said, instead calling it a time for "compassion."
Jones was a bakery worker, grandmother and mother of five, according to ABC station WLS-TV in Chicago.
Chicago police said it "extends its deepest condolences to the victim’s family and friends."
Police said at 4:25 a.m. Saturday, officers responded to a domestic disturbance and were "confronted by a combative subject."
"Upon arrival, officers were confronted by a combative subject resulting in the discharging of the officer's weapon, fatally wounding two individuals," the statement said.
The medical examiner's office identified those killed as Jones and a 19-year-old man.
Janet Cooksey, who said her son was the 19-year-old killed in the shooting, said he wasn't an "angry" or "violent" child.
"No mother should have to bury her child," she said at a news conference.
The incident is being investigated by the Independent Police Review Authority, police said, and officers involved will be placed on routine administrative duties for 30 days.
"This new policy which was implemented by Superintendent [John] Escalante, will ensure separation from field duties while training and fitness for duty requirements can be conducted," police said in the statement. "Going forward, this will be standard protocol following all officer-involved shootings."
A separate police-involved shooting was reported in Chicago later that day. Chicago police said officers responded to an “assault in progress” Saturday afternoon and found a man with a gun. The man "was confronted by police" and "an officer discharged his service weapon striking the offender," said police.
The man was taken to a hospital to undergo surgery, police said. The gun was recovered at the scene, said police.
Chicago Mayor Rahm Emanuel said today, "There are serious questions about yesterday’s shootings that must be answered in full by the Independent Police Review Authority’s investigation. While their investigation is underway, we must also make real changes within our police department today and it is clear changes are needed to how officers respond to mental health crises.
"This afternoon I directed the new Acting Chief Administrator of the Independent Police Review Authority and the Interim Superintendent of Police to meet with each other as soon as possible to review the Crisis Intervention Team training, around how officers respond to mental health crisis calls," he added. "I have asked that they determine the deficiencies in the current training, and determine what steps can be taken immediately to address them.”
The mayor's words come amid a federal civil rights investigation into the Chicago Police Department that's looking into how the department disciplines officers as well as patterns of racial disparity in the use of force.
The investigation began after dash cam video was released last month showing white Chicago police officer Jason Van Dyke shooting black 17-year-old Laquan McDonald 16 times in Oct. 2014. Van Dyke allegedly kept firing after McDonald already hit the ground.
The video's release led to the resignation of Chicago Police Superintendent Garry McCarthy and calls for Emanuel to step down.
The Associated Press contributed to this report.