Family members held a press conference following Saturday's police shootings of Bettie Jones, 55, a mother of five, and Quintonio LeGrier, a 19-year-old engineering student.
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Both were shot and killed after police were called to a private residence in response to a call about a domestic dispute.
News reports said the teen struggled with mental health issues, and had been threatening his father with a baseball bat.
A short time after arriving on the scene, police opened fire, striking LeGrier, who they said was charging down the stairs carrying the bat.
Jones, LeGrier's downstairs neighbor, who opened the door for officers as they arrived, also was struck by a police bullet and died Saturday at the hospital.
Separately, police fatally shot another man within hours of the other two shootings, according to news reports, some of which said the man was armed but had dropped his weapon and had his arms raised when police opened fire.
Many in this midwestern city, already reeling from other recent incidents in which police are said to have been too ready to pull the trigger on their service weapons,condemned the shooting.
"This needs to stop," LeGrier's mother Janet Cooksey told reporters Sunday.
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"No mother should have to bury her child, especially under these circumstances. The police are supposed to serve and protect us," Cooksey said through tears. "Is it a badge to kill?"
She added, at the press conference attended by a couple dozen people, that her son was "a good child" and an honor student.
"Seven times my son was shot, once in the buttocks that showed he was turning away," said the grieving woman said.
"This needs to stop. No mother should have to bury her child."
Bettie Jones' nephew, Jahmal Cole, in an interview with CNN, described her as a church-going grandmother and community pillar.
Cole said young college student Quintonio LeGrier "was trying to make a difference, and he was a role model -- not only to the people in his community but to his family."
The Chicago police, he continued, "used deadly force in a situation where it was not called for, and I think that there needs to be some swift justice."
The shootings come with 's police already under federal investigation over a video that shows a white police officer shooting a black teen 16 times, with most of the gunshots fired as the boy was lying motionless on the ground.
The shooting of 17-year old Laquan McDonald, which took place in 2014, has triggered a federal civil rights probe into the police and calls in some corners for the resignation of the city's mayor, Rahm Emanuel, a former top White House aide to President Barack Obama.
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News reports said that Emanuel at present is on a family vacation in Cuba, but his office released a statement after this weekend's shooting promising that the incident will be investigated.
"Any time an officer uses force the public deserves answers, and regardless of the circumstances, we all grieve any time there is a loss of life in our city," the statement read.
"All evidence will be shared with the Cook County State's Attorney's Office for additional review in the days ahead."
Emanuel recently fired Chicago's police chief and pledged the city's "complete cooperation" with the federal probe into the actions of its embattled police force.
The police meanwhile, in a terse statement, expressed regret over the shooting of Jones, which they said was a tragic accident.
"The 55-year-old female victim was accidentally struck and tragically killed. The department extends its deepest condolences to the victim's family and friends," the police department said.
An earlier statement said that after receiving the initial report of the domestic dispute, said that "officers were confronted by a combative subject resulting in the discharging of the officer's weapon, fatally wounding two individuals."
Police referred all questions to the Independent Police Review Authority, the agency that investigates possible police misconduct.
Police tactics and racism have been the subject of a national debate since protests erupted in Ferguson, Missouri, in mid-2014 over the shooting death of a black teenager, 18-year-old Michael Brown.
On Sunday, interim IPRA chief Sharon Fairley told reporters that her investigators "went promptly" to the crime scenes to interview witnesses and collect evidence.
"Our objectives are to conduct thorough and timely investigations of each incident," Fairley said, giving no additional information.
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