Leaked audio captured Jurado, who is running against incumbent Kevin de León for the District 14 seat, quoting the lyrics to the song "F- Tha Police" by West Coast hip-hop group N.W.A. at a meeting with students at Cal State L.A.
Jurado was asked about abolishing the police.
"What's the rap verse? F- the police, that's how I see 'em," Jurado responded.
On Sunday, several widows, family members and girlfriends of fallen LAPD officers spoke about the pain, anger, and frustration they experienced after hearing Jurado's remarks.
"For someone who wants a position in city council to say those words ... it's dangerous," said Angela Mendoza, who described Jurado's remarks as a "slap in the face."
Mendoza's boyfriend, LAPD Ofc. Fernando Arroyos, was shot and killed while the two were shopping for houses. Arroyos was off duty at the time, but she says the shooters opened fire after seeing his police ID.
Jurado released a statement Sunday, saying voters are looking for someone who will take a "fresh approach to public safety."
"I understand the pain that families feel after the loss of a loved one, and I have deep respect for anyone who has lost someone in the line of duty," she said. "We can honor the memories of fallen officers while also pushing for accountability and equity in policing, and real investment in our communities.
What I'm hearing from voters is a desire for new leaders who will take a fresh approach to public safety because what we've been doing clearly isn't working. That's what we're focused on, and we won't be deterred by attempts to take us off course."
Last week, Eyewitness News learned that the Cal State L.A student who asked Jurado the question about policing works for De León's city council office.
It's unclear whether that student is the person who recorded Jurado's answer to the question.
In 2022, De León found himself in the middle of a different leaked audio scandal, which involved racist remarks and resulted in the resignation of City Council President Nury Martinez. De León resisted calls to step down.
He has accused Jurado of being a police abolitionist.
De León discussed the matter last week, saying he "supports our men and women in blue who protect us every single day, especially in the neighborhoods where folks want more police presence."
"It's not a reflection of the values of who we are in the city of Los Angeles."
"The police budget is one of the largest budgets in the entire city of Los Angeles, so you have to engage with them. If you come into a legislative branch like city council completely hostile and you want to abolish them, then what does that say about public safety for everyday folks in Los Angeles?"
Over the weekend, about two dozen residents from neighborhoods across District 14 gathered outside Jurado's Highland Park home to demand an apology for her remarks.
The final day of voting in the race is Nov. 5.