The department, known as the LAPD, confirmed to The Epoch Times that officials deployed a patrol unit to Martinez's home.
"The Los Angeles Police Department deployed a patrol unit to the home of Nury Martinez following a series of protests, in which Ms Martinez was concerned about her safety," a spokeswoman said in an email.
"This decision was made by the Chief of Police to keep those units in place, for the safety of the Councilwoman and her family."
A spokesman for Martinez, a Democrat, didn't return requests for comment before publication.
The detail decreased to 14 hours a day as of May 6, the sources said.
Det. Jamie McBride, the director of the Los Angeles Police Protective League, the LAPD’s union, told the broadcaster: "It’s kind of ironic. Here she is demanding $150 million be reallocated from the police budget, but yet she has security at her house by the Los Angeles Police Department."
Every unit taken away for the detail is one less unit to respond to a 911 call, he said.
Rick Coca, a spokesman for the City Council president, confirmed the detail to Spectrum. Martinez, he said, had received death threats, as had her daughter.
“LAPD recommended that placing a detail at her home was the best course of action to ensure the safety of the Council President and her family," he said in a statement.
The detail was canceled recently because Martinez felt the security was compromised, Coca added later.
The motion Martinez introduced with support from Los Angeles Mayor Eric Garcetti, a Democrat, said the funding cuts were being made “as we reset our priorities in the wake of the murder of” George Floyd, the black man who died in policy custody last month in Minneapolis.
The motion says the city’s administrative officer and chief legislative analyst, with help from the mayor, should work to identify “at least” $100 to $150 million in cuts from the LAPD’s budget.
The money should be redirected “back into disadvantages [sic] communities and communities of color,” the motion stated.
The LAPD in a statement said it was working with city officials to figure out where the cuts will come from.
But the Los Angeles Police Department Command Officers Association said in a separate statement that the motion included language "indirectly accusing the police department of systemic racism."
"Instead of reaching out to the Command Officers Association as many council members have done in the past to address concerns or advise of their pending actions and allow for the opportunity to come together as professionals to discuss issues, Council Member Martinez simply tweeted their intentions," it said.
The motion, the group charged, "is extremely irresponsible and risks the safety of all Angelenos," asserting it will lead to victims of crimes such as domestic violence waiting longer for a police response.