(CNN) An Australian woman killed last weekend by Minneapolis police "didn't have to die," the city's police chief said Thursday.

"This should not have happened," Chief Janeé Harteau said in her first public comments since Justine Ruszczyk, 40, was killed Saturday, minutes after calling police to report a possible sexual assault near her home. "On our squad cars, you will find the words: 'To protect with courage and serve with compassion.' This did not happen."

Harteau couldn't address the fatal shooting in person earlier because she was away backpacking in the mountains and could not return sooner, she said.

The police chief said she spoke to Ruszczyk's fiancé on Thursday morning and told him the shooting shouldn't have happened. She also pledged to strengthen the department's body camera policy, including exploring new technology that could activate officers' body cameras when their squad car lights are turned on.

Neither the squad car's dashcam nor either of the officers' body cameras was on at the time of Ruszczyk's shooting, officials said.

"It is my belief that the body cameras should've been activated," Harteau said, based on information she's received from the Minnesota Bureau of Criminal Apprehension, dubbed BCA. "My expectation is that our policy is followed."

Harteau said Noor was fully trained and performed very well in his field training. She said her opinions on the shooting were based on the information released so far by the BCA.

"I believe the actions in question go against who we are as a department, how we train and the expectations we have for our officers," she said. "These were the actions and judgment of one individual."

She assured Ruszczyk's family, the community and Australians "that I will do everything in my power to make sure due process is followed and justice is served."

Family hires attorney experienced in police shootings

Ruszczyk's relatives say they're still stunned the bride-to-be was killed by police -- and they've hired an attorney with experience handling police-involved shootings.

"We are still trying to come to terms with this tragedy, and we are struggling to understand how and why this could happen," the family said in the statement released to CNN affiliate Sky News Australia

"All we want to do is bring Justine home to Australia to farewell her in her hometown among family and friends. In the meantime, we ask that you give us time to grieve in private and to support each other at this very difficult time."

Justine Ruszczyk, 40, was killed one month before her wedding.

Ruszczyk, who moved to the United States in 2014, was set to marry her fiancé, Don Damond, next month.

The Ruszczyk family's attorney is calling for a comprehensive investigation and policy review.

"The family is interested in justice in (the) largest sense -- an unbiased, transparent investigation, necessary changes in police training, officer selection criteria and practice, proper and nondiscretionary policies on usage of forensic tools, including squad and body cameras, swift and sure discipline and full and complete recompense," Robert Bennett told CNN in an email Thursday.

Bennett has represented families in police-involved shootings in the Minneapolis area. He was among attorneys for the family of Philando Castile , who was killed last year by St. Anthony Officer Jeronimo Yanez.

Ruszczyk's death also has attracted wide coverage, and her family and friends have demanded answers, though it could be months before Minnesota authorities finish their investigation.

911 calls lead to police encounter

Some of the first clues emerged this week about what may have led to the police shooting of Ruszczyk.

She made two 911 calls Saturday night to report a possible sexual assault near her home, according to transcripts the city released Wednesday.

"I can hear someone out the back and I, I'm not sure if she's having sex or being raped," Ruszczyk said in the first call.

"... And I think she just yelled out 'help,' but it's difficult. The sound has been going on for a while, but I think, I don't think she's enjoying it," Ruszczyk said.

The dispatcher told her police would arrive soon.

Eight minutes later, Ruszczyk called 911 again, saying officers had not arrived. At 11:35 p.m., the dispatcher told her police were on the way.

Officers Harrity and Noor arrived on the scene a short time later.

As they drove down the alley in their squad car, Harrity heard a loud sound that startled him, the officer told the BCA, the agency said.

That's when Ruszczyk approached Harrity's driver's-side window, Harrity told investigators. Noor, sitting in the passenger seat, fired his gun and shot Ruszczyk through the driver's-side window, Harrity said.

Audio: Officers scrambled to save woman's life

Immediately after Ruszczyk was shot, both officers got out of the car and tried to save her, Harrity told investigators, according to the BCA.

Dispatch audio from the officers captured the anxiety as they waited for an ambulance to arrive.

"(Squad) 530, uh, shots fired," one of the officers says. "Can we get EMS code 3, Washburn and 51st Street? We've got one down."

The dispatcher then calls for other units, and an officer -- it's not clear which -- says someone is starting CPR.

An officer tells other units they are in the entrance of an alleyway between houses.

The dispatcher asks the officer on the radio whether the situation is under control, and whether the ambulance can safely approach the shooting scene.

The officer says it's safe. "There are no suspects at large," he says.

Later, an officer's voice gets increasingly tense while waiting for the ambulance.

"Where is EMS on this?" he says.

The audio was provided to CNN by the operator of Minnesota PoliceClips, a company that monitors and records police radio dispatches.

Neither police nor the city of Minneapolis communications department would verify the authenticity of the recording.

Answers slow

For days, Ruszczyk's family and Minneapolis' mayor have expressed mounting frustration about the slow trickle of information from the BCA.

Noor has invoked his right not to speak to investigators, the agency said Tuesday.

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But Minneapolis Mayor Betsy Hodges has urged Noor to issue a statement.

"He has a story to tell that no one else can tell," she said. "We can't compel him by law, but I wish that he would make that statement."

The case is also hampered by the lack of video footage from the dashcam and body cameras.

Harteau, the police chief, said the department has had the body cameras for about eight months, "so it's not second nature" yet for officers to activate them. The department wants to do everything it can with its training and policy to ensure that officers do activate the cameras before arriving to a scene, she said.

Investigators also want to talk with a man on a bicycle who watched police perform CPR on Ruszczyk and are asking him to come forward.

It could take two to four months before the BCA finishes its investigation, said Chuck Laszewski, a spokesman for Hennepin County Attorney Mike Freeman's office.

Freeman then will decide whether either officer involved should be charged in Ruszczyk's death.

Castile's mother: 'This is not a black or white thing'

In recounting her conversation with Damond, Harteau said Ruszczyk's fiancé expressed concern and fear the community may have in calling 911.

"Although disheartening, I understand the fear, and why it exists," she said. "This has had a negative impact on the community trust we've built."

She pledged to try to regain that trust.

People flooded the streets later Thursday for a march in Ruszczyk's memory. Castile's mother, Valerie, was among those in attendance.

Before the march, she met Damond outside his home. They stood with their arms around each other.

Ruszczyk "was murdered on my son's birthday," Valerie Castile told CNN. "So, it's symbolic for us, and we had to come out and support her, because like I said after the verdict, they were going to kill again -- and they have."

"The spirit of my son led us over here to speak with the family and march in this march today," Castile said.

The march drew supporters of all races. Some chanted, "Prosecute the police, no justice, no peace."

"They're beginning to understand this is not a black or white thing," Castile said. "This is a human being thing."