Emanuel issued the statement the day after a Chicago officer fatally shot Bettie Jones, 55, and Quintonio LeGrier, 19, while answering a call about a domestic disturbance.
"There are serious questions about yesterday's shootings that must be answered in full by the Independent Police Review Authority's investigation," Emanuel said. "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."
Emanuel, under fire for a series of fatal police shootings, directed the department and the leaders of the independent Police Review Authority and the police department to meet immediately to "determine the deficiencies in the current training, and determine what steps can be taken immediately to address them."
Mother says son shot seven times
Family members and supporters of LeGrier and Jones are blaming bad leadership and a police culture of "shoot first and ask questions later" for the deaths. Specifically, they asked why police didn't use non-lethal force, such as stun guns.
"What about the Tasers?" asked Jacqueline Walker, a friend of Jones, as she joined a crowd Sunday afternoon in front of the residence where the shootings happened. "Taser him down, don't start shooting people, innocent people."
Police said an officer shot LeGrier, who was carrying a metal bat and acting in a "combative" manner, early Saturday morning while responding to a call about a domestic disturbance. Jones, a neighbor, was "accidentally struck and tragically killed," police said.
The shootings come as police in Chicago and across the nation are being scrutinized for the use of deadly force.
LeGrier's mother, Janet Cooksey, said Sunday that police shot her son seven times, once in buttocks. That meant he was turning away, she said.
"This needs to stop," Cooksey said, tears streaming down her face as she addressed reporters.. "No mother should have to bury her child, especially under these circumstances. The police are supposed to serve and protect us."
She was surrounded by supporters, some who wore T-shirts saying "Rahm failed us."
"When is the mayor going to step up?" she asked. "When are we going to get some help?"
Standing outside a modest home with beige siding and white-trimmed windows, several other people echoed Cooksey's sentiments.
Jahmal Cole, who described himself as a spokesman for the organization My Block, My Hood, My City,
said he is Jones' nephew.
"What happened should matter to everyone," he declared. "Everyone was celebrating Christmas like any other family. She should not have to be shot down just coming to the door. Your family does not want to wake up to news like this."
Police say the incident began when the teen threatened his father with an aluminum bat. The father called police and then called his downstairs neighbor, Jones, to open the door when officers arrived, CNN affiliate WLS reported.
LeGrier was charging down the stairs still carrying the bat, the affiliate reported. Police opened fire, and both LeGrier and Jones were shot.
The Cook County Medical Examiner told CNN on Sunday that Jones died of a gunshot wound to the chest and LeGrier died of multiple gunshot wounds. Both deaths were ruled homicides, the medical examiner said.
Other details, such as how many shots were fired, were not released by authorities. It's not known if any video of the shootings exists.
The officer will be on administrative duty for 30 days while an independent police review authority investigates, Chicago police said. He has not been identified.
"The department extends its deepest condolences to the victim's family and friends," the police department said in a statement.
'Where was the Taser?'
Cheryl Dorsey, a retired Los Angeles police sergeant and law enforcement consultant for CNN, also wondered why police didn't use stun guns.
"Where was the Taser?" she said. "Why didn't they deploy a Taser? If they didn't have one on scene, they should have had one with an officer who was responding as backup. What was the urgency? There was no exigent circumstance that the officers could not have waited until a Taser arrived on scene."
Dorsey said an aluminum bat could cause injury but "is not a deadly force."
She said "deadly force should have been used (by police) as a last resort and not a first resort."
'He was an honors student'
Jones was a mother of five and a grandmother who loved church and music, WLS reported.
LeGrier's family said the Northern Illinois University student suffered from a mental illness, WLS had reported, but on Sunday Cooksey disputed that characterization.
"Stop disparaging his character," she pleaded Sunday. "He does not have mental issues. He was an honors student."
"We should not be here right now," Cole chimed in. "A 19-year-old honor student was shot down by police -- taken away from his family -- and he didn't have a gun. That is a problem," he said.
"What do you want?" a reporter asked.
"Justice," was the reply, almost in unison, as all the men gathered around the microphone.
'An act of war'
Mark Carter, who said he supported Jones and LeGrier's families, said there's a mental health crisis within the Chicago Police Department.
"A lot of people with mental problems are drawn to this work. Everyone is not meant to be a police officer," Carter said.
In a tone decidedly more defiant than other participants, Carter said, "You are calling for an act of war and that's what you'll get. You are crossing a line that you do not want to deal with in this city if you keep killing our children."
Follows protests against Chicago police
The shooting came two days after protests against Chicago police officers' actions
-- including the killing of black teenager Laquan McDonald -- shut down parts of the Magnificent Mile, a high-end shopping district in the city.
"Sixteen shots and a cover-up!" the Christmas Eve protesters chanted.
They were referring to the fact it took 13 months before authorities released surveillance video of the 17-year-old's shooting
. Jason Van Dyke, the white Chicago police officer who killed the teenager, was charged with first-degree murder. Van Dyke -- who has a history of complaints against him
, mostly for excessive force -- has pleaded not guilty.
That case contributed to Garry McCarthy losing his job as Chicago's police superintendent
and spurred calls for Emanuel to resign
. The graphic nature of the video, in which Van Dyke is shown shooting McDonald not long after arriving on the scene, didn't help. Nor did the fact that this footage didn't square with other officers' accounts on the scene.
Homicides overall, not just officer-involved shootings, have been a major issue in Chicago. The city has had more homicides in the past few years than New York and Los Angeles, which are more populous cities.
Emanuel acknowledged the public discontent in a speech earlier this month, saying his city needs "a painful and honest reckoning
into what went wrong" in the McDonald case and beyond.
The mayor has already welcomed a U.S. Justice Department investigation
into whether Chicago police have made a habit of violating the law.
"We will be a better city for it," Emanuel said. "It is in our self-interest, because we need (federal) assistance to make the fundamental and necessary changes."